The Italian has already admitted City need "a miracle" to salvage their campaign after taking just one point from their opening three group games, with Tuesday's visit of the Dutch champions.
And he pointed to Chelsea's decade-long struggle to lift Europe's elite trophy as he warned supporters they could face a long wait for the ultimate piece of silverware.
"I don't think that we are ready to win the Champions League," Mancini said." If we say this, we are not honest.
"We are a good team. We are not ready like the other teams.
"Chelsea tried for 10 years to win the Champions League. They were probably the best team in Europe for 10 years and they won it after 10 years, probably when they didn't deserve to.
"They deserved to win it three or four years before. The Champions League is like this.
"If we are very good, we are fantastic, we win the next three games, everything can happen. But, before, the way is very long."
After Ajax City face Real Madrid at home and Borussia Dortmund away.
"The players owe me three big performances," he added. "We have less chance of qualifying for the next round but, when you're a top team, even when you're out, you should play 100 per cent in every game."