The Blues saw their lead at the top of the Premier League cut to just one point after losing 2-1 at Tottenham last Saturday, while United grabbed a last-gasp winner at Manchester rivals, City.
United will go back to the top of the table, for 24 hours at least, with victory over Spurs on Saturday, while Chelsea host Stoke on Sunday.
And Scotland international Fletcher believes the pressure is on Carlo Ancelotti’s men to prevent United claiming a fourth successive title.
“They are the team leading the league and all the pressure is on them,” he said. “We are just taking care of ourselves.
“It just shows you in one weekend things can change.”