Victory saw reigning Premier League champions City climb above Southampton into second place and move to within six points of leaders Chelsea.
“I am very pleased,” Pellegrini told Sky Sports.
“We beat a very good team. They were second in the table and deserved that position.
“We played a very good game, it was important to have a clean sheet again.
“They had just one chance in the 90 minutes and that is important for the trust in our team, and to score three goals against the best defence is also very important,” the Chilean added.
Yaya Toure opened the scoring in the 51st minute at St Mary’s Stadium before centre-back Mangala was sent off for a second bookable offence.
Goals in the final 10 minutes from substitute Frank Lampard and Gael Clichy secured victory for the visitors.
Despite an ultimately convincing scoreline, some of the shine of victory was removed for City after a late injury to Vincent Kompany meant they finished the game down to nine men.
“We cannot know if Vincent Kompany has a problem with his hamstring, we will see with the doctor tomorrow,” Pellegrini said. “It was a precaution, we will see if it is a cramp or injury.”
This loss represented a first home defeat since April for Southampton, the surprise package of the Premier League season so far.
“You know that if you do some mistakes you are punished for that,” said Southampton manager Ronald Koeman.
“It was not good enough today and we have to realise that. The difference was the quality,” the former Dutch international added.
Chelsea, who remained unbeaten, dropped points for only the third time this season after they were held to a goalless draw at Sunderland on Saturday.
“It was a difficult match,” said Chelsea manager Jose Mourinho. “Only one team tried to win from the beginning, the other team didn’t. They defended a lot and they defended well.”
Liverpool ended their three-match losing streak as Glen Johnson’s late goal clinched a hard-fought 1-0 success against Stoke at Anfield.
“The players were absolutely incredible,” said Liverpool manager Brendan Rodgers. “We fully deserved it and to keep a clean sheet against a very good side was pleasing.”
Robin van Persie scored only his fourth goal for Manchester United this season as the hosts cruised to a 3-0 win over Hull at Old Trafford.
“It was the best match of our season. What pleased me most was the way we dominated the game from the first minute to the last minute,” said United manager Louis van Gaal.
Meanwhile Danny Welbeck returned from injury to maintain Arsenal’s recent revival as the England striker sealed a 1-0 win at West Bromwich Albion.