City cut United's Premier League lead to five points with five games left in midweek after the champions lost 1-0 at lowly Wigan Athletic and Mancini's side thumped West Bromwich Albion 4-0.
Afterwards the Italian ruled his side out of the title running despite their success and has not changed his mind in the days since.
"We are normal, we are not on the moon. Like all normal people we make mistakes. They [United] are fantastic, they have won everything, but we are here," he told a news conference before Saturday's trip to in-form Norwich City.
"I think we should be proud of our job at this moment as this is the best season since 1968 when Manchester City won the championship."
City could reduce United's advantage to two points with victory given Sir Alex Ferguson's under-pressure team do not host Aston Villa until Sunday.
"I'm happy if he wants to stay but if he wants to stay he should change his mind [behaviour]," the manager said.
"Yaya is getting better, we will decide tomorrow for Yaya," Mancini added.
