No Premier League club have allowed more goals than Stoke this season.
"It is very hard to talk to the fans at this moment as they are hurting like us", Carvalhal said.
Swansea City have officially been relegated from the Premier League after seven seasons in the top flight. Wolves are looking for a keeper with plenty of experience, and Jack Butland has that, and the shot stopper is looking to stay in the Premier League after Stoke's relegation.
Swansea will be relegated from the Premier League on Sunday unless they beat bottom side Stoke City, in addition to a heavy defeat for Southampton against champions Manchester City that leads to a swing in goal difference of 10.
"Our recruitment strategy hasn't been good enough, we all recognise that and the blame for it ultimately rests with ourselves. Perhaps the club has lost its unique identity, the special essence that made Swansea City different - better, in many ways - and we need to rediscover that identity both on the pitch and off it if we are to make the community proud of this football club again".
The Swans had been close to the drop on several occasions in recent years and, despite an initial revival under Carvalhal, they were unable to produce another escape.
Carvalhal, however, believes the results under his predecessor Paul Clement were the cause for Swansea's relegation.
"Whether it is with me or not, we will see".
"Everyone was sad, but it now has changed because we have a game". We recognise the huge role the club plays in the community and its importance.
After the Swansea victory, Lambert said that they were in need of a rebuild for next season.
The Welsh club were promoted from the Championship in 2011, beating Reading 4-2 in a pulsating play-off final, but their stay in the top-flight has now come to an end.
Supporters protested before Sunday's defeat against Stoke, calling for the removal of chairman Huw Jenkins and unhappy at the running of the club since Kaplan and Levien led an American consortium's takeover of the club in 2016.
The 52-year-old will now take a few days out to reflect on the season before deciding whether he wants to have another go next term.