The England international secured a point for the Gunners with his 74th-minute curler after Bruno Fernandes had put the Red Devils ahead.
Nevertheless, he revealed that his perfectly executed tackle on Rasmus Højlund – which prevented United from taking the lead – was his best moment at Old Trafford.
“Probably the tackle, just because of the state of the game,” Rice told Arsenal website.
“It defines the small margins in football for me because it could have been a penalty and probably a red card for me if I didn’t react as quickly as I did.
“I made the tackle, and we go to the other end and nearly score. These are the margins in football, but for me, those tackles are equally as important as scoring goals. That was a big one today so I liked that.”
Rice, who has been impressive for Arsenal this season, is expected to play a key role when Mikel Arteta’s men face PSV in the Champions League later this week.