Solskjaer is now the bookies' favourite to be the next Premier League manager to lose his job after a humiliating 5-0 defeat at home to rivals Liverpool.
The Norwegian is in his third full season at the club and yet to lift any silverware, and winning one looks further away than ever after a humbling loss at Old Trafford.
Solskjaer is a club legend at United thanks to his six league titles as a player, but came into the job on a caretaker basis with an uninspiring CV.
The former Molde and Cardiff boss won supporters over with some early stellar performances, but former Liverpool midfielder Murphy believes Solskjaer isn't good enough to compete at the top.
"I think sometimes you have to just accept your level," Murphy said.
"You give it a go, you do your best, it's a bit like when you're a player.
"When you play, you try to be the best player in the world, you try to be the best in your position.
"You reach the level you get to and then you kind of work out where you are, and you know what your strengths and weaknesses are."
Murphy believes Solskjaer has now reached that point, and simply cannot compete with the likes of Klopp, Guardiola and Thomas Tuchel, with their sides setting the pace in the Premier League title race thanks to some scintillating displays.
United now sit in seventh place and are winless in their past four league games, and things won't be getting any easier.
The Red Devils face Tottenham, Manchester City, Chelsea and Arsenal in their next five Premier League games, which could spell disaster for Solskjaer judging by his team's recent performances.
Murphy acknowledges that the 48-year-old has had good moments during his return to Manchester, but compares it to his own playing career, saying you have to know your limitations.
He explained: "You have good games along the way, like Ole's had some good games where he's set up a tactical plan and beat Man City a couple of times.
"They've had some moments, PSG, but ultimately, week in week out, he can't compete with the managers he's up against.
"It's a bit like me playing against Gerrard and Vieira every week.
"I'll give it my best, I will, I'll try and on the odd day I'll get the better of them, but more often than not they're going to dominate me because they're better."