The Amsterdam club have revived their Champions League campaign, after losing their opening two Group D matches, by taking four points from back-to-back games against City.
Ajax, boasting a core of homegrown players, won 3-1 in the Dutch capital a fortnight ago and then claimed a creditable 2-2 draw against the expensively-assembled Barclays Premier League winners at the Etihad Stadium.
They still face a tough task to qualify from a group that also includes Real Madrid and Borussia Dortmund but they are firmly in contention ahead of remaining games against the Spanish and German sides.
Former Liverpool winger Babel said: "It was a statement to the other teams.
"We have to analyse what the gameplan will be for the next two games but I think these two games will give us confidence.
"We have to take it step by step but I think we made a little statement."
Ajax led 2-0 at Eastlands after two goals from Siem de Jong inside the opening 17 minutes.
Yaya Toure pulled one back soon after and City levelled 16 minutes from time through Sergio Aguero.
De Jong tested City goalkeeper Joe Hart twice in the second half but Ajax were fortunate to come through a frantic finish.
Aguero had a second goal disallowed for a marginal offside by Aleksandar Kolarov after 88 minutes and Mario Balotelli had an injury-time penalty appeal declined.
Babel said: "I think it was a tough match.
"It was a different game from the game against City at home. They pushed a lot from the start.
"Fortunately we scored the two early goals but we still had to keep the focus.
"You know City are going to come more attacking and we almost lost it with the offside goal at the end.
"Maybe we had a bit of luck. It was marginal - sometimes they can be good for them but in this case it was good for us.
"It was a positive result."
Ajax are third in the group and even finishing in that position - and so earning a place in the Europa League - would be a positive outcome for the side initially ranked as the outsiders of the quartet.
Holland international Babel said: "I think our goal is to stay in Europe, either the Champions League or the Europa League.
"We have to analyse the next game and after that we will decide what our chances are for Europe."
Babel, 25, is hoping to revive his career back with his first club after a disappointing three-and-a-half years at Anfield and another unsuccessful stint at Hoffenheim.
Despite his past troubles, he was pleased to be back in England.
"It is always great to be back," said Babel, who cost Liverpool £11.5million in 2007.
"English fans and the English atmospheres are special. I have missed it."