City had won just once in six games before the international break and were knocked out of the League Cup, fell eight points behind Premier League leaders Chelsea and saw their Champions League challenge all but ended at the hands of CSKA Moscow.
Things looked to be following a familiar pattern against Swansea when they fell behind at the Etihad Stadium to Wilfried Bony’s early goal.
They hit back, however, through Stevan Jovetic and a trademark effort from powerhouse midfielder Yaya Toure and are now one point behind second placed Southampton, who play Aston Villa on Monday, and eight behind unbeaten leaders Chelsea who beat West Bromwich Albion 2-0.
“We are absolutely confident the way we play and sure that we are going to win the game,” Pellegrini told the BBC.
“Very happy because we won the game. We played very well and had a lot of chances to score the third goal and we defended well.
“We have to play seven games more before the end of December and we have to fight for all of them.”
Before the game Pellegrini talked of the crucial need to win their remaining eight Premier League games of the calendar year to maintain pressure on leaders Chelsea.
After last season’s November international break, City embarked on a stunning run of 20 games unbeaten in all competitions, winning 18, and it is likely they will have to produce a similar run this season.
“We have had two weeks to clear our heads and I think the performance was good other than the first 20 minutes. It was a really big win,” captain Vincent Kompany told the BBC.
“Given the last month we will take a win and it is good we are creating chances again. We have given ourselves a challenge but football is made of challenges. We can get a lot of good out of this year.”
Manchester City host Bayern Munich in the Champions League on Tuesday before a trip to Southampton next Sunday.
(Reporting By Tom Hayward; editing by Toby Davis)