City kept themselves firmly on course to win the race for fourth place in the Barclays Premier League with Sunday's 2-1 victory over West Ham at Eastlands.
The result means that with four fixtures to go, Mancini's side are seven points clear of nearest rivals Liverpool - who have played a game more - in fifth and Tottenham in sixth.
The Blues' Holy Grail is within touching distance, but their manager is adamant his players must keep working hard all the way up to the end of the campaign.
"We can only relax after May 22, not before," Mancini said. "We should try to get the maximum number of points that we can. I think after what we have done, we deserve to be in the Champions League, but we have another four games - it is not finished. We are not under pressure, but we know we have a big chance.
"Our target at the start of the season was the Champions League and now, we are in a good way. We are in fourth position and have seven points over Tottenham and Liverpool - and we will play the FA Cup final (against Stoke on May 14)."
Source: PA
Source: PA