"It was probably the right decision," Rooney was quoted as saying on the BBC website. "Of course I did (apologise)."
Rooney, who said he would not appeal the decision, will be unavailable for his club until the derby against Manchester City on Nov. 2 as he received an automatic three-match ban for the dismissal.
Rooney's challenge was described as "crazy and irresponsible" by West Ham manager Sam Allardyce while Manchester United's Louis van Gaal backed referee Lee Mason's decision.
"I saw the West Ham player making a counter-attack and I tried to break-up the play, but I just misjudged it," Rooney said.
"I am just grateful that the lads were able to hold on."
Rooney's team sealed a 2-1 win despite playing the last 30 minutes with 10 men.