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.
Controversial striker Mario Balotelli is never far from the headlines and misses the Norwich game as he is still suspended for being sent off against Arsenal last weekend.
Mancini has a strained relationship with his 21-year-old compatriot but he is not definitely up for sale.
"I'm happy if he wants to stay but if he wants to stay he should change his mind [behaviour]," the manager said.
With Balotelli out, Carlos Tevez could play again having faced West Brom in his first start since refusing to warm up as a substitute during a Champions League game in September. The Argentine striker ended up an outcast before a recent apology.
Midfield dynamo Yaya Toure, whose driving runs are sorely missed by City when he is not playing, could return from injury at Carrow Road.
"Yaya is getting better, we will decide tomorrow for Yaya," Mancini added.
