Here's the issue:
Jews today observe the Passover meal on Nisan 15 rather than 14. Obviously some of the Jews in Jesus' day did so as well. Jesus celebrated on Nisan 14 with his disciples.

Scripture to consider on this issue:
First of all, keep in mind that the Jewish days begin at sunset. Since the approximate time (it varies) of sunset in Jerusalem around Passover is 6:00 p.m., let's refer to this sunset for the purposes of discussion as 6:00 p.m. When the Hebrews were leaving Egypt, they were instructed to "kill it in the evening" in reference to the Passover lamb (Exodus 12:6). Now does that mean they kill the lamb before 6:00 p.m. on Nisan 14 just prior to Nisan 15, or did they kill the Passover lamb after 6:00 p.m. at the beginning of Nisan 14 just after Nisan 13? From the passage in Exodus 12, it seems that the latter is correct. As a matter of fact, that's when Jesus observed the Passover prior to his crucifixion, at the very beginning of Nisan 14. The next day (which was still Nisan 14) Jesus was crucified. However, take a look at John 18:28, "Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover." So, on the day of the crucifixion after Jesus had observed the Passover the previous evening, there were Jews who were still anticipating the observance of their Passover meal.

Nisan 15 was the beginning of the Feast of Unleavened Bread according to Lev. 23:6, "And on the fifteenth day of the same month is the feast of unleavened bread unto the LORD: seven days ye must eat unleavened bread." In that same passage we know that separately and distinctly was the observance of the Passover on Nisan 14 as we see in Lev. 23:5, "In the fourteenth day of the first month at even is the LORD’S passover." So, the question is this: Did the eating of unleavened bread in observance of the Feast of Unleavened Bread begin the day after the Passover meal, or does it include the Passover meal? Here's a clue: Exodus 12:18, "In the first month, on the fourteenth day of the month at even, ye shall eat unleavened bread, until the one and twentieth day of the month at even." Counting 14 to 21 inclusive, you get 8 days altogether, but that's counting the Passover meal on the evening of Nisan 14, "Exodus 12:8 And they shall eat the flesh in that night, roast with fire, and unleavened bread; and with bitter herbs they shall eat it."

So, how did the justification to merge the first day of the Feast of Unleavened Bread with the Passover Feast come about? It is impossible to say for certain, but we do see a change in the Passover procedure in Deuteronomy 16:1-8. At the time of this writing, Moses and the Hebrews are camped on the east side of the Jordan River preparing to move into Canaan. Previously, the Passover Feast had been observed within one's own home with one's own family. However, here in Deuteronomy, we see that a new procedure shall be observed going forward, seen in Deuteronomy 16:2, "Thou shalt therefore sacrifice the passover unto the LORD thy God, of the flock and the herd, in the place which the LORD shall choose to place his name there." Going forward, the Passover will be observed at a central location - no longer in one's own home. Since this annual festival now involved a trip to the location of the tabernacle/temple, it may be here that many of the Jews merged the two feasts together making the first day of the Feast of Unleavened Bread on Nisan 15 to be also the celebration of the Passover Feast.

Consider these two verses:

Mark 14:12 And the first day of unleavened bread, when they killed the passover, his disciples said unto him, Where wilt thou that we go and prepare that thou mayest eat the passover? Luke 22:7 Then came the day of unleavened bread, when the passover must be killed.

It is obvious from these two verses that it had become common practice to refer to Nisan 14, the day the passover lamb was killed, as the first day of unleavened bread. This is probably due to the fact that unleavened bread was also eaten with the passover meal as well as the seven days that followed.

Conclusion:
It appears that it was standard practice to observe the Passover meal either way in the first century. I say so because there is never a question raised from Jesus' disciples about observing the Passover meal when they did, nor does John's gospel give us any explanation regarding why the Jews in John 18:28 observed the Passover meal the next evening. Strictly speaking, however, the scripture text we've observed seems to clearly indicate that the correct time to observe the Passover meal was when Jesus did, at the very beginning of Nisan 14 in the evening. After all, on how many issues from the Law of Moses were the Jewish leaders NOT confused about in Jesus' day? So, who are you going with? Jesus...or the ones who crucified him?

Other passages to read for additional information:

Luke 22:7-9
Then came the day of unleavened bread, when the passover must be killed. And he sent Peter and John, saying, Go and prepare us the passover, that we may eat. And they said unto him, Where wilt thou that we prepare?
 
Luke 22:15-16
And he said unto them, With desire I have desired to eat this passover with you before I suffer: For I say unto you, I will not any more eat thereof, until it be fulfilled in the kingdom of God.
 
John 18:28
Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover.
 
John 18:39
But ye have a custom, that I should release unto you one at the passover: will ye therefore that I release unto you the King of the Jews?
 
John 19:14
And it was the preparation of the passover, and about the sixth hour: and he saith unto the Jews, Behold your King!
 
Mark 14:12
And the first day of unleavened bread, when they killed the passover, his disciples said unto him, Where wilt thou that we go and prepare that thou mayest eat the passover?
 
John 11:55-56
And the Jews' passover was nigh at hand: and many went out of the country up to Jerusalem before the passover, to purify themselves. Then sought they for Jesus, and spake among themselves, as they stood in the temple, What think ye, that he will not come to the feast?

Matt 26:4-5
And consulted that they might take Jesus by subtilty, and kill him. But they said, Not on the feast day, lest there be an uproar among the people.