Manchester United have won 22 of their 45 matches this season
United reached the FA Cup final on Sunday, but needed penalties to beat Championship side Coventry, despite leading 3-0 with 20 minutes to go at Wembley.
They are seventh in the Premier League, 16 points off the top four, and were eliminated in the Champions League group stage this season.
"I really don’t know where Ten Hag goes from this," said Sutton.
"It is the end for him now - there is no way he is coming back after that."
Former Newcastle and Manchester City goalkeeper Shay Given agreed, saying: "The writing is definitely on the wall for him.
"It doesn’t look good for him - he looked lost at times on the touchline. There is a lot of noise around the club at the moment."
-- Courtesy of BBC Sport