"44 He said to them, “This is what I told you while I was still with you: Everything must be fulfilled that is written about me in the Law of Moses, the Prophets and the Psalms.”
45 Then he opened their minds so they could understand the Scriptures. 46 He told them, “This is what is written: The Messiah will suffer and rise from the dead on the third day, 47 and repentance for the forgiveness of sins will be preached in his name to all nations, beginning at Jerusalem. 48 You are witnesses of these things."
When you actually look at the passage in question carefully, it is important to note the following:
1. Jesus is alluding to several passages of the TANAKH rather than a direct quotation. That is first and foremost.
2. In Verse 45, Jesus is taking the disciples through each passage one by one, speaking specifically of certain passages which we can assume from the NT as a whole were the same passages he alluded to. He is demonstrating how and why he fulfills those passages.
3. When Jesus says it is written, he means that the scriptures as a whole are teaching the message he is giving in verses 46-48. This links back to point 1, Jesus is stating that his mission is written in the scriptures because of them pointing to him.
There is no case of forgery being mentioned in the following passages if you understand the point that Jesus is getting at.
Hope this helps.
Addendum: Some have suggested that Jesus is using Midrash, a form of interpretation within Rabbinic thought. However this can be debated.