The Red Devils looked to be heading for an embarrassing derby defeat following goals from Vincent Kompany and Ilkay Gundogan.
However, Manchester United were able to level the Premier League clash thanks to Paul Pogba’s quick-fire brace at The Etihad.
England international Chris Smalling scored the winner with a close-range finish to complete the comeback at the Eastlands outfit.
Manchester United are 13 points adrift of runaway Premier League leaders Manchester City despite their brilliant derby win.
The Red Devils signed Chile international Alexis Sanchez in a swap deal from Arsenal in the January transfer window.
Former Manchester United star Giggs believes Mourinho’s men can challenge for the title next term with some shrewd additions.
“Well they have to (improve),” Giggs told Matchday Live. “They have to next year, they have to do that.
“Otherwise, City will win the league again, because of the quality that they’ve got, the transfer window, they’re going to improve, they’re going to get better players.
“Every season, whoever wins the Premier League, the teams beneath them have to improve. So Manchester United have to next year.””
Manchester United finished in sixth place in the Premier League table last term but won the Europa League and the League Cup under Mourinho last term.
The Red Devils haven’t won the Premier League title since 2013 when Sir Alex Ferguson got his hands on his 13th and final top-flight crown.
Manchester United lost 2-1 to La Liga giants Sevilla in the Champions League round of 16.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news