City entertain Tottenham on Wednesday evening knowing victory would leave them needing to win their final match at West Ham on Sunday to seal a place in next season's Champions League.
However, the Blues are also aware defeat would consign them to the Europa League and leave them waiting a little longer to join Europe's top table.
"It will be a big mistake from players if they don't want to come because we have not finished fourth," said Mancini.
"In the future Manchester City will be a fantastic team."
After ending Aston Villa's own Champions League bid at the weekend, the Blues are in optimistic mood, with Gareth Barry in line for a recall after recovering from a hamstring injury that forced him to miss the encounter against his former club.
Barry is one of a number of players brought to City by former boss Mark Hughes, who paid the price for a series of unconvincing displays by losing his job just before Christmas.
But even if the Italian is celebrating at the weekend, he will spare a thought for the man he replaced.
"Mark Hughes worked here for the first five months of the season and worked very well," he said.
"If we get fourth position he deserves 50% of the credit because I think he worked well.
"I have worked for five months and he has worked for five months. The season has been split between us."
Source: PA
Source: PA