The Rugby Park club are the first club since Partick Thistle in 2018 to be demoted from second bottom place of the top flight. They now face their first second tier campaign since 1992-3 just two seasons after finishing third in the Premiership under Scotland manager Steve Clarke.
Wright has two years left of his contract. “Listen, I'm raw at the minute,” he said. “I know I'll get the support of the board. It's not my future that needs to be discussed tonight.
“I'm more concerned about the people who work in the background of this club and the people of the town. That's my concern tonight. My future will be sorted.
“There's a rebuild job now. I think there's only four or five signed players now. One or two others may have been getting contracts even if we went down. I might have to revisit that.”
Wright was appointed in February after Alex Dyer’s sacking and with Kilmarnock sitting in tenth place. “Listen I will take responsibility for my time here,” he said. “I do think I have done OK up to a point. But you cannot win games when you make the individual errors we did and we have done it for far too long.”
Unhappy supporters gathered outside Rugby Park after the defeat. Two early goals from Danny Mullen and Lee Ashcroft put Dundee 2-0 up after 12 minutes. A Kyle Lafferty second-half penalty halved the deficit on the night but there was still too much left to do to retrieve the tie. Wright was baffled by how ineffective Kilmarnock were over the 180 minutes.
“It surprised me on Thursday, it shocked me tonight because I didn't think we could be that bad again, and we were,” he said.
“I just feel sorry for them,” Wright added, with reference to the fans. “I've let them down and ultimately the players have let themselves and let the club down. But I'll take my responsibility myself as well. I'm not ducking anything. I thought I could get us out of it but unfortunately I didn't.”