Memphis, who joined United last year from PSV Eindhoven, has found it hard to settle in England, scoring twice in 19 league games, but Rooney defended the 21-year-old.
"I think we're all disappointed," Rooney told the Manchester Evening News.
"Memphis is a fantastic player and that happens, we all give bad passes away. A lot of things happened from when you give the ball away to when they've scored the goal, so I don't think we can stand here and blame Memphis."
Rooney said United had allowed Chelsea to seize the initiative after Jesse Lingard put the visitors ahead in the second half.
"The game was broken up a bit, we gave too many free kicks away and then we couldn't get up the pitch," he said.
"But with Chelsea, at times it's difficult, because they pushed players up front and they didn't really play with any system, so it's difficult to work out how to defend against them."
The draw left United fifth in the table, six points adrift of the top four.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
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