The Red Devils were beaten 2-1 by the Spanish champions in the Round of 16 second leg to bow out of the competition 3-2 on aggregate with Sir Alex Ferguson opting to go with Danny Welbeck alongside Robin van Persie instead of Rooney.
Stoke City striker Owen, who left Old Trafford at the end of last season, suggested that Rooney may be feeling a little down about the omission and has urged him to change the managers plans going forward.
"For Rooney not to start is a real kick in the teeth and it's got to be a big worry for him," Owen told TalkSPORT.
"It's the biggest game of the season and the manager has shuffled his pack and not included him.
"Wayne will take it one of two ways.
"He will either get his head down, try to improve and force his way back into the team, or he'll think, 'The manager has not picked me for the biggest game, he obviously doesn't fancy me', and it might not be the end of the story."
Owen added: "When I was at Manchester United their relationship was very good, they talked, shared jokes and there were no problems whatsoever.
"I would be surprised if it was something of that nature [a falling-out], but the decision to leave him out isn't going to help if it is that."