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City head into Tuesday's match with Stoke seven points behind leaders Manchester United after both teams secured victories on Saturday.
Mancini's side lost two of four league matches, including a defeat by United, in December.
But they responded to a surprise 1-0 loss at Sunderland to pick up a 4-3 win at Norwich City that was all the more impressive due to an early red card for Samir Nasri.
Ever since the 3-2 loss to United, Mancini has maintained that, with half of the season remaining, there is no need to panic and that Alex Ferguson's team's Champions League commitments will affect them in the new year.
His task is set to grow even harder, with Yaya Toure and Kolo Toure departing for the Africa Cup of Nations after the FA Cup tie with Watford on Saturday.
But Mancini has set his sights on still being in touch with United by the time the Ivory Coast duo return, and the Italian is adamant that even United's current advantage should not be seen as intimidating.
"It's not important to look at the table because it's not final, but we need only to work, to win and then maybe we'll look again at the table in February," he said.
"With 10 players, it's difficult. Norwich are a good team but we showed we are there for the title. We fight for every game. The guys were fantastic against Norwich."
Edin Dzeko scored a brace in the victory at Norwich and the Bosnian international believes the victory showed City's staying power.
"There's still a lot of games to play," said the former Wolfsburg striker.
"We lost the last game against Sunderland. We were unlucky, we couldn't find the goal, but against Norwich we fought from the first to the 90th minute.
"Everyone wants to play and I was back (against Norwich) and I gave the maximum."
Jack Rodwell and Micah Richards remain on the injured list for Mancini, while Maicon is also out with a knee problem and Mario Balotelli is doubtful with illness.
City have not won at the Britannia Stadium in six visits since the Potters were promoted to the Premier League, but Mancini's side have found Stoke a much easier proposition at home, with four straight wins against Tony Pulis' men.
Stoke striker Kenwyne Jones hailed his side's team spirit after they came from 3-1 down with 10 men to draw 3-3 with Southampton on Saturday and he believes they will now travel to Manchester on a high.
Jones scored Stoke's first goal on Saturday before Matthew Upson and Cameron Jerome helped Pulis' side claim an unlikely point, which extended the Potters' unbeaten run to nine matches.
"We had a few slip-ups, but credit to the team, manager and the fans for the run we have been on," said Jones.
"The next game is the most important game for us because we're going to the home of the champions. We're going to prepare again, try and be solid, and see what happens.
"Everyone knows what Stoke City is about and they have seen it time and time again for however long.
"Why would we feel sorry for ourselves? We've never done that in games, so why would we do it now?
"Here at Stoke City, we play for 90 minutes. If we get beat, we get beat, but we'll never give up.
"That comes from pride. This is our job. No-one wants to lose, so you're not just going to stand there and accept defeat."
Rory Delap and Marc Wilson remain long-term absentees for Pulis.
