Paolo Di Canio insists that Sunderland would have been relegated if it wasn't for him.
The Italian took over from Martin O'Neill at the end of March, and he helped turn their fortunes around including their biggest derby win over Newcastle in more than 50 years.
"I have to be honest, yes I think we would have gone down," said the Italian.
"In my opinion this team was down. Some people said I would be too hard and would stress the players but we have recovered mental energy.
"Stephane Sessegnon, one goal in six games. Under me two goals in four games. Improvement.
"Under me, 1.3 points per game instead of one point per game. We would have finished top 10. Improvement.
"Eight points in six games without a striker. With Steven Fletcher, the top scorer injured. [Skipper Lee] Cattermole out for a long time. This is part of the job.
"Only the future can tell if I'm right but I think Paolo Di Canio will be right. I hope we can celebrate one day."
Di Canio also gave his backing to friend and compatriot Roberto Mancini after he was sacked at Manchester City.
"It's not easy when you've got big egos like Carlos Tevez. With Mancini he had a simple difficulty: he had seven top hot-headed footballers. One or two you can handle, but not seven," he said.
"Also players are piranhas. They smell if you are weak. Mancini started something political with the board. The players knew. They saw a fault-line. It was easy for them to say 'now we relax'. If they think you are weak it will change the dynamic."
The Swans will round off arguably the finest season in their 101-year history when they face Fulham at the Liberty Stadium on Sunday.
Laudrup's side are guaranteed a top-10 finish in the Premier League and also secured the Capital One Cup, their first major piece of silverware, in February.
The Dane's calm and dignified approach has won him many admirers this season, and even reportedly attracted the interest of the likes of Chelsea and Real Madrid.
And defender Williams has spoken of how, far from utilising the 'hairdryer' treatment Sir Alex Fergsuon is well known for, Laudrup's cool demeanour even extends to how he reacts to a poor performance.
"He never loses his temper or raises his voice," said the Wales captain.
"If he feels like that, or he is unhappy with how we play, he just doesn't speak to us.
"He doesn't come in the dressing room, we don't see him so I presume those are the times he would have lost his head. He is very composed.
"In Britain we are used to managers coming in and going nuts.
"Even with Brendan (Rodgers), who was pretty composed, we saw him lose his head a few times, but never with this manager.
"He always tries to be calm and composed when he speaks, he tries to look at the positives and we just don't see him sometimes if we have lost."
It was not all plain sailing for Laudrup as Swansea had an inconsistent start to the season, before a League Cup win over former boss Rodgers at Anfield acted as the catalyst for an excellent run of results, culminating in victory over Bradford at Wembley.
Williams admits the adjustment to Laudrup's methods took time, but has nothing but praise for the former Barcelona and Real Madrid midfielder.
"It was different when he came in," he said. "It took some time for everyone because they (Laudrup and Rodgers) were total opposites of each other in terms of how they worked from day to day.
"It took a while to get used to it, but we have enjoyed the year with him. He gives us plenty of leeway, he works differently to Brendan, but we enjoy working with him and he is an easy going guy.
"We have embraced that and he is fun to work for.
"He has definitely given the players more responsibility, especially the senior players, we make a lot more decisions off the field about how we want to do things.
"That was a shock at first as we were used to being told what to do, where to go and at what times, and he left it down to us.
"I have enjoyed that responsibility. It has been a big year for the senior lads in terms of looking out for the younger players and the lads coming in from other countries.
"I have enjoyed it, being as responsible as I can around the team."
Rooney has been given permission to sit out the trip as wife Coleen is due to give birth to the couple's second child.
The 27-year-old's Old Trafford future is in doubt after he asked for a transfer recently.
Sir Alex Ferguson has now passed that matter on to new manager David Moyes to deal with.
However, after being left out of Ferguson's final home game before retirement last week, it is understood Rooney will also miss the Scot's final one ever as a manager at The Hawthorns this afternoon.