Stoke have appointed Gary Rowett as their new manager on a three-year deal.
2017 SeasonAll times ET
Swansea announced on Friday that they would not renew Carvalhal's expiring contract, with news of Lambert's departure coming soon afterwards.
Swansea's relegation from the Premier League was confirmed as Stoke won 2-1 at the Liberty Stadium.
"It's there for everybody to see at the end of the day. I was their most successful Premier League manager," Hughes said.
Goalkeeper said Oliver had "a garbage bin for a heart" and later told Italian television that he stood by his comments.
Stoke's owners have admitted they made "significant errors" this season, in the wake of the club's relegation from the Premier League.
Stoke City midfielder Charlie Adam says some of his teammates were "getting away with murder for a long time" with their lack of effort.
Jack Butland has described some Stoke City players as "ill-disciplined" who manager Paul Lambert couldn't "rely on."
Paul Lambert declared himself "gutted for everybody at the club'' after Stoke's relegation before backing them to "rebuild and be really strong."
In some respects the surprise is not that Stoke City have been relegated, but more that they spent a decade in the Premier League.
A pair of second-half goals doomed Stoke City to the second tier for the first time in more than a decade with a 2-1 home loss to Crystal Palace.
Xherdan Shaqiri is set to hold talks with Stoke over his future after the end of the season.
Stoke boss Paul Lambert has joked that £35 million would only be enough to buy one of Jack Butland's hands.
Stoke forward Jese Rodriguez has been given unpaid compassionate leave until the end of the season, the Premier League club have confirmed.
Liverpool are limping over the line for a place in next season's Champions League after drawing against a relegation-threatened team yet again.
Liverpool dropped points against a relegation threatened side for a second successive week as they played out a goalless draw with Stoke.
Stoke have been making recruitment plans for the Championship but manager Paul Lambert insists he is not yet resigned to losing any players.
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|Brighton & Hove Albion||38||9||13||16||-20||40|
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