Owen is baffled why some former United players have been so public in their criticism of the appointment of Carrick as a caretaker and his chances of landing the job outright.
"I can't believe people are questioning whether he should get the job," Owen said on the The Wayne Rooney Show.
"Manchester United have waited about 12 years - they've gone for proven, legends, everything since Sir Alex (Ferguson).
"And the one time they are starting to play well, get results, the fans are on board - you're telling me at the end of the season if he gets third (place) they will say 'thanks, but no thanks'. How is that possible?"
Rooney also said, "Everyone at Manchester United loves Michael Carrick and they are just scared it doesn't go right. He's done an unbelievable job."