The Dutchman expressed delight with his side's performance in their 3-1 victory over the Premier League champions on Wednesday evening at the Amsterdam ArenA
The Amsterdam outfit found themselves one down thanks to Samir Nasri's first-half strike but turned things round as Siem De Jong, Niklas Moisander and Christian Eriksen got on the scoresheet.
And after the game De Boer expressed his belief that the Dutch champions were just too strong for their Premier League counterparts.
He told reporters: "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.
"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."
Goalscorer De Jong was similarly pleased with the performance but remained keen to stress that his side still have work to do to seal qualification for the knockout stages.
He added: "We expected a lot of danger from them, because they have so much quality in front. They scored on their first chance, while we were the better team.
"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."