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 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.
Paul Scholes will start for Manchester United as Ferguson looks for the midfielder's experience to help settle his side.
"We did the right thing resting Paul Scholes - he'll play on Sunday. He's shown his influence since he came back," Ferguson told a news conference on Friday.
Scholes retired at the end of last season but was tempted back by Ferguson in January because of a lack of fit players in midfield, although the former England man has continued to be a first choice even with the injury list easing.
His precision passing and occasional eye for goal led Ferguson to label Scholes as one of the best midfielders in the last 20 years, which goes some way to explaining why United struggled to replace him in the close season.
Bids for Inter Milan's Dutch playmaker Wesley Sneijder were denied by United but their recall of Scholes and general lack of flair has prompted pundits to say this could be one of the worst United sides to win the Premier League title.
They are not quite there yet after Wednesday's wobble but Ferguson believes the championship experience of Scholes and Co means an immediate recovery is likely.
"We were disappointed to lose but we have to put it into perspective. In the treble year (1999) we went through the whole season from December without losing. A couple of years back we lost 4-1 at home to Liverpool and won the league by nine points," he said.
"From the position of a few months ago to where we are today, we have to be delighted. Sunday is very important and we must get back on track. A great thing about our club is we do recover and we have to do that again."
Villa are not totally safe from relegation and manager Alex McLeish, who played for Ferguson at Aberdeen, is under pressure from fans after struggling to mould a youthful winning side since his shock move from bitter city rivals Birmingham City.
"They are probably safe but you never know, McLeish is a very capable manager. He's had some criticism from fans but has handled it very well," Ferguson said.
"I've known him since he was a little kid. He was always a very receptive and intelligent young man. He was a great player and had a good career. He did a great job for Scotland and at Birmingham, and will do a good job at Villa given time."
Bottom club Wolverhampton Wanderers could be all but relegated if they lose at Sunderland but there is still genuine hope for some of the other sides scrapping in the basement.
Queen's Park Rangers, two points above the bottom three, could go a long way towards ensuring top flight safety if they win at West Brom on Saturday while Blackburn Rovers would move out of the bottom three with victory at Swansea City.