The Dutch outfit are currently bottom of Group D having lost their opening two matches to Real Madrid and Borussia Dortmund.
The Amsterdam club host the Premier League champions in their next game, and De Boer is hoping to take some points from the fixture.
"If we want to survive in Europe we need a result from this match and that's our goal," said De Boer.
"Against Madrid we played a bad match, they're good opponents but we were well below our level. Our team is learning so let's hope they are quick students. We must have confidence that we can perform much better and if we do that, we can get some points.
"It's always difficult to put your finger on why City aren't performing like they are in the Premier League. Maybe it's a bit like Dortmund last year; they played great in the Bundesliga but didn't do very well in the Champions League. Things can change very quickly in this team because they have so much quality. If we play our game, with the philosophy we have, we can maybe get a good result."
Ajax host City at the Amsterdam ArenA on Wednesday night.