Poirot lied about fingerprints being found, in order to provoke the culprit into a confession. He did not fake any physical evidence. When he says "I put that part in for you", or in the original "I put that in to please you", he's saying that he inserted a false statement into the story. This is quite a well-worn trope, even in 1936, but it is still a nice bit of drama.
Christie's original expresses the same idea as in the simplified version, but the language is naturally more idiomatic and nuanced:
"That fingerprint clinched things, Poirot," I said thoughtfully. "He went all to pieces when you mentioned that."
"Yes, they are useful - fingerprints."
He added thoughtfully:
"I put that in to please you, mon ami."
"But, Poirot," I cried, "wasn't it true?
"Not in the least, mon ami," said Hercule Poirot.
The part about "to please you" relates to earlier conversations between Hastings and Poirot about the nature of their task. Poirot's approach is mainly psychological, not just because he uses his brain (the famous "little grey cells") but because he works by trying to understand what sort of person would do this sort of crime. Hastings is often more hopeful of finding some surprise piece of physical evidence which will let them make progress. For Poirot, the evidence helps to reveal the character of the criminal, but he does not expect it to contain an easy answer.
At the beginning of Chapter 8 there is another episode which shows some of the same factors in play. Poirot deceives Hastings in the style of a prank, and criticizes his interest in "clues". I don't know how this was rendered in your edition, but mine has this text:
"The crime," said Poirot, "was committed by a man of medium height with red hair and a cast in the left eye. He limps slightly on the right foot and has a mole just below the shoulder-blade."
"Poirot?" I cried.
For a moment I was completely taken in. Then the twinkle in my friend's eye undeceived me.
"Poirot!" I said again, this time in reproach.
"Mon ami, what will you? You fix upon me a look of doglike devotion and demand of me a pronouncement à la Sherlock Holmes! Now for the truth - I do not know what the murderer looks like, nor where he lives, nor how to set hands upon him."
"If only he had left some clue," I murmured.
"Yes, the clue - it is always the clue that attracts you. Alas that he did not smoke the cigarette and leave the ash, and then step in it with a shoe that has nails of a curious pattern. No - he is not so obliging. [...] We are confronted here by an unknown personage. He is in the dark and seeks to remain in the dark. But in the very nature of things he cannot help throwing light on himself. In one sense we know nothing about him - in another sense we know already a good deal."
And Poirot goes on to describe his impression of the killer's personality. The theme comes up again elsewhere too. When Poirot admits that he made up the finding of a fingerprint, he is again gently making fun of (what he sees as) Hastings' interest in finding straightforward conclusive evidence.