Manuel Pellegrini admitted Manchester City did not deserve to beat Swansea City following their 2-1 Premier League victory on Saturday.
Having seen Wilfried Bony's 26th-minute header cancelled out by Bafetimbi Gomis' 90th-minute equaliser, City appeared set to drop two points at the Etihad Stadium.
However, Pellegrini's men - who were coming off a 4-2 Champions League success against Borussia Monchengladbach in midweek that saw them top Group D - took the three points courtesy of a huge slice of luck in the second minute of stoppage time.
Yaya Toure's shot took a big deflection off Kelechi Iheanacho and ballooned into the net, sending City, at least temporarily, back to the top of the table.
"Once again this team demonstrated character to go to try to win the game," Pellegrini told Sky Sports. "We really didn't play well during the whole game, I think that Swansea made a very good game.
"I was worried before the game because I knew that three of our players were not 100 per cent recovered, especially Kevin [De Bruyne] that couldn't play, David [Silva] that could play just 60 minutes and after you have an important achievement as we did in the week, also to restart the motivation in this game is not easy.
"Maybe we didn't deserve to have the points, but I think that these points maybe replace the three points we lost against West Ham where we had at least 18 or 20 chances to score.
"It was a very important week, a very critical moment in the Premier League because we played very bad against Stoke [in a 2-0 loss last weekend] and a very important achievement to finish at the top of the group in the Champions League.
"So I think that it was very important we finish here with the win and the three points - now we have a complete week to recover and I'm sure the performance of the team will be better against Arsenal."
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