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, a result which 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.
"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."
He added: "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)."
City took the lead against the Hammers through Nigel de Jong in the 10th minute and appeared to be cruising to victory when Pablo Zabaleta doubled their advantage shortly afterwards. Demba Ba pulled a goal back for the visitors in the 33rd minute, though, and City then missed a series of chances to make it 3-1.
It eventually turned out that their early double was enough, but it could and maybe should have been a more comfortable triumph against the league's bottom side and Mancini admitted his team may have been guilty of thinking their job was already done after the opening 15 minutes.
"Probably after these two goals we thought it was finished, but it never is until the referee blows the final whistle,'' said Mancini, who also confirmed that De Jong had come off at half-time merely as a precaution with a view to next weekend's clash with Everton, and that an ankle knock picked up by Zabaleta was not serious.
Although the loss was West Ham's fifth in a row, leaving the Hammers three points from safety with as many games remaining, their manager Avram Grant is staying upbeat.
"We made a very bad start - in the first 20 minutes we were not in the game, they had scored two goals and could have scored more,'' Grant said. "We had a great comeback and showed a lot of spirit and the character of the team, and we made it 2-1 - also Robbie Keane had a big chance.
"In the second half we could have done some more, so there were a lot of positives to take for the next games, which are the most important ones."
Source: PA
Source: PA