Carvalhal pondering his future at relegated Swansea
The Swans required a huge turnaround on the final day of the season to stay up at Southampton's expense, but a 2-1 defeat at home to already-demoted Stoke City spelled the end of a seven-year top-flight stint.
Although there were reports earlier in the week that Carvalhal will not take the club forward, he claims Swansea have asked him to stay on as manager, although outlined why he is not yet ready to make a decision.
"I talked with the owners [on Saturday], we will talk again on Monday," he told BBC Sport. "I will think about Swansea and myself.
"I must talk with my family. After that, I will make the right decision about my future.
"I know the Championship and reached the play-offs twice. It's not common for a team to reach the play-offs two years in a row. In this moment, I must breathe. Afterwards, I will think about that."
It ends in defeat at the Liberty. Our seven-year @premierleague adventure comes to an end… pic.twitter.com/PWpPs81yDA
— Swansea City AFC (@SwansOfficial) May 13, 2018
And defender Angel Rangel, who is to depart, called on the Swansea board to ensure the club return swiftly to the top flight.
"It was an emotional day - all we wanted was to win for the fans," he said. "We knew it was impossible to stay up. We lost
"I'm proud of what I achieved for the club, but it's bitter. It's mixed feelings. It's been the hardest season.
"From start to finish we have been down there. It's been unfortunate, because it's such a great club. We need to build again.
"I think the club can get back. The board have to give that joy back to the fans."