Supporters of the Premier League champions were delighted with the Argentine's display during their 2-1 win over Garry Monk's men.
Many City fans picked the defender as their man of the match as Manuel Pellegrini's side beat Swansea City 2-1 in the Premier League after he kept Wilfried Bony relatively quiet throughout the game.
The Swans striker did give the visitors the lead but Demichelis stopped him from doing further damage and goals from Stevan Jovetic and Yaya Toure secured victory at the Etihad Stadium.
Before the game, Pellegrini said his side could not afford to lose again this calendar year, having dropped points at Queens Park Rangers in their last league fixture.
After the match, meanwhile, he told BBC Sport: "I am 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.
"It was a difficult start because they scored with their only chance in the first half. We are absolutely confident in the way we play and sure we are going to win the game.
"If we scored the third goal we could play well and not so tight. We had the chances but didn't score. We have to play seven games more before the end of December and we have to fight for all of them."
Here's how Manchester City fans reacted to Demichelis's display on Twitter...
Important win today. Not back to our best by any means, but much improved! Thought Clichy and Demichelis were excellent! #mcfc— Matthew Yarwood (@MPY123) November 22, 2014
MCFC World (@MCFCworld) November 22, 2014
Demichelis MOM today. Outstanding on Bony who is an absolute beast! #MCFC— Robert Jones (@bobby_jones_10) November 22, 2014