The Sunday Supplement panel questioned whether David Moyes has recovered from his failed spell at Manchester United, and think he must show "leadership" to bring Sunderland back into the Premier League.
Moyes was sacked in April 2014 after just 10 months in charge of United - the third shortest managerial stint in the club's history.
He then had an unsuccessful year at Real Sociedad before being appointed Sunderland manager last summer.
Moyes said on his arrival at the Stadium of Light that the club would be fighting relegation again, and that fight proved unsuccessful as defeat against Bournemouth on Saturday ended their 10-year stay in the Premier League.
"There is a lack of leadership at the club," said the Daily Telegraph's Jason Burt on the Sunday Supplement. "An experienced manager like Moyes could give that leadership to a degree, but I think he has lacked leadership.
"It was quite clear last season that Sam Allardyce was driving the club forward and trying to save them, but the impression I get with Moyes is there have been too many excuses and reasons why they are going to fail, rather than succeed, so I think he has to take responsibility for that.
"Personally I don't think he has recovered from Manchester United, he's not the same guy, he hasn't got the same confidence or belief in himself. Sociedad too - that's three failures in a row now. He has to stay and get them up, if he leaves I don't know where he goes."
Moyes said on Saturday that he hopes to lead the club back into the top flight, and Burt thinks he must now be the driving force at Sunderland.
"He has to offer to stay," he said. "He always says it takes him a while to get things going and if he has any belief in himself than he has to offer to stay and turn it around.
"He is not going to get a better club than Sunderland. The ownership issue is the big thing. Either they sell the club and get a new owner, or they think they have to go again and organise the club and give the manager what he wants.
"Moyes has to take control and say this is what has to happen to get us back in the Premier League. I am prepared to do this, let me do this. The onus is on him to take control rather than wait and see what the club want to do."
The Times' Matt Dickinson agreed with Burt that Moyes appears to have been damaged by his spell in charge of Manchester United.
"When you have been scorched with something like Manchester United, when you fail on that scale, you are battered in such a way that it takes years to recover. We have seen several England managers struggle to get their mojo and belief in themselves back," he said.
"I am sure he would deny it but I think it takes a big chunk out of you. Manchester United is a huge job and it was brutally tough.
"He has an opportunity and didn't make the most of it. When you fail in a job of that exposure it would knock anyone's conviction. Unless you are absolute certain of every decision it's an impossible job and it leaves bruises that last for years."