The former Holland international said that the Premier League outfit "had no answers" to Ajax's play throughout the game.
"I know what we are capable of. I think we saw a good Ajax today that wanted to show something good. We played quite good sometimes," he said.
"City didn't have an answer to our play. There was a difficult time for us, but we after that, we picked it up again and deserved the 2-1."
De Boer went on to say that his side will have to work hard to qualify from Group D, but is confident of achieving a result when the two sides meet in Manchester.
He added: "I'm glad we scored the equaliser before half-time. We had a lot of space in the second half, so we could play our game. Now we should get a result in Manchester, or else this result isn't much worth."