Ex-Man Utd players say Ten Hag is out of time after Palace drubbing
United's record 13th league defeat of the campaign left them eighth and facing the prospect of having no European football next season. They have conceded 81 goals in all competitions, their worst showing since the 1976/77 season.
"Tonight felt like the final nail in the coffin," ex-United midfielder Paul Scholes told Premier League Productions.
"There was a lack of know-how from the team, a lack of effort which is the big disappointing thing.
"I've felt he might get another year and work for a club that has calmed down a little bit by the new owners but it just doesn't feel like it now. It's quite plain to see it feels like borrowed time."
Michael Owen, who played for United from 2009-12, said the club's board should cut their losses and sack Ten Hag before the end of the season, with an FA Cup final against Manchester City still to play for.
"He cannot, simply cannot, manage the team next season," Owen said.
"I just wonder, there's just so much at stake, even if it's only for four games, I wonder whether the board might just have to try to do something here and now and be quite radical about it."
United have three league games left, hosting leaders Arsenal and sixth-placed Newcastle United in their next two matches before winding up the campaign at Brighton & Hove Albion.
Ex-United defender Ashley Young said the club might fail to win any of their remaining games.
"It's shambolic, everything about United's defending was crazy," he told Sky Sports.
"If United put on displays like they have shown tonight, they will miss out."