Speaking on Sky Sports on Sunday, Jamie Carragher said: "Mark Robins famously kept a Manchester United manager's job.
"I think that result against Coventry has just cost a Man United manager his job. I don't see how Erik ten Hag stays.
"It's just performance after performance. It's probably the most-embarrassed dressing room of a team that has just won a big game.
"What is it about Ten Hag that makes you think he's going to take Man United forward next season? I just don't see it."
Man United managed to avoid a disaster on Sunday, beating Coventry City on penalties despite going 3–0 up in the second half at Wembley.
The Red Devils are now one game away from winning the FA Cup but there are still many questions about Ten Hag's long-term future at Old Trafford.