City led by three goals going into the final few minutes after Sergio Aguero's early opener and a goal in each half from Yaya Toure, the second of which came from the spot.
But Costel Pantilimon's own goal and an injury-time strike from substitute Victor Anichebe gave the scoreline a closer look and Pellegrini acknowledged that his team might have relaxed too soon.
"It was not as close a game as the scoreline says," said the City boss, who must have been relieved to see his team show some away form after four defeats on the road. "But perhaps all of us were thinking about the next game.
"We didn't plan to go more defensive but I think the game was more easy than we'd thought so we became more relaxed in the final minutes.
"They scored two goals in the last four minutes and so the scoreline says 3-2 but I think we had more of an advantage than that."
Vincent Kompany returned to the team after an injury-hit season thus far and Pellegrini welcomed seeing his star defender back on the pitch.
"He's a very important player for us," added the Chilean. "He's our captain. He played with no problem and we gave him the 90 minutes."
Meanwhile, Aguero's neat finish took him to 17 goals for the season and Pellegrini had a word of praise for the Argentine forward.
"Sergio is playing very well," he said. "It's an important amount of goals but more important is for the team to win.
"That's why I subbed him today because we have to play another game in less than 72 hours against another strong team in Southampton."