United were dumped out of the FA Cup by Leicester City on Sunday.
“United competing in the Europa League is not good enough, first and foremost, the fans know that, the club know that and Ole knows that," Murphy told TalkSport.
“Not progressing in the Champions League was a massive, massive blow for them. Yes, they're going to get in the top four… but so they damn should!
“He's in a position for me where the Europa League, for me, has become monumental for him and the club.
“I like him and I'm not one who wants to see managers sacked and I do think they've made some strides forward, but Manchester United have to be doing better.
“If they don't win the Europa League and only finish in the top four then I think they'll make a change."