Despite having several of the world's costliest footballers in their ranks, the Premier League champions have struggled to make an impact in Europe's flagship competition and are bottom of Group D.
Defeat at home to the Dutch league champions would torpedo any lingering hopes City have of qualifying for the knockout stages and represent a second consecutive early exit.
"I don't think we're ready to win the Champions League," Mancini told reporters after his team stuttered to a 0-0 draw at West Ham United on Saturday.
"If we say we're ready to win it, we're not honest. In the Champions League it's clear that incredible situations can happen in February and March but we've been drawn in a tough group this year, like last year."
City's last outing in Europe ended in a 3-1 defeat in Amsterdam two weeks ago and that result, together with a 3-2 defeat at Real Madrid and a 1-1 home draw with Borussia Dortmund, has left their future in the competition dangling by a thread.
Mancini's team have also looked unimpressive in their last three Premier League games, scraping wins against West Bromwich Albion and Swansea City before Saturday's stalemate with West Ham.
"We're a good team but we're not ready in the Champions League, like the other teams. Chelsea tried for 10 years to win the Champions League," Mancini said.
"They were probably the best team in Europe for 10 years and they won it [this year] 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 win our next three games, then fantastic... anything can happen. But the road is very long."
