But the Northern Irishman – who was only appointed back in February – insists it is his players who must take a long, hard look at themselves after their feeble attempt at overturning last week's 2-1 first-leg defeat at Dens.

Their hopes of escaping relegation were done inside 12 minutes of the Rugby Park return as goals from Danny Mullen and former Killie defender Lee Ashcroft sealed another 2-1 win for James McPake's team – and the fate of Wright's side, who did pull one back with a Kyle Lafferty penalty.

As a group of fans gathered outside the ground to protest against the club's head of football operations James Fowler, Wright said: "I just feel sorry for them.

"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.

"We didn't do enough. We didn't compete enough. Dundee were stronger but they didn't have to do a lot to win either game.

"We gifted them three out of four goals.

"The first goal tonight is absolutely embarrassing from our point of view. No-one took responsibility and we end up behind the eight-ball within the first 15 minutes.

"The second goal is a wee bit unfortunate because Kirk (Broadfoot) and Zeno (Rossi) collide and leave a free header for Ashcroft.

"Too many players haven't turned up and not just in the play-off games – it's all season.

"That's 24 defeats this season in 40 games if you count this as two league games in. That says a lot about the squad.

"We've been gifting goals away. The first day I arrived I told them if they do the basics, defend well and take responsibility you can stay in the league.

"But we haven't done that. They haven't done it all season.

"It takes a mental capacity to see out games that you're not doing well in and to fight for your team.

"But it hasn't happened here for a period of time.

"It surprised me on Thursday that Dundee were hungrier – it shocked me tonight because I didn't think we could be that bad again, and we were.

"We've got what we deserved."

While Wright – who still has two years left on his Killie deal – is now left to mull over what comes next, McPake is dreaming of his club's return to the big time.

The Dundee boss, who was handed the job after the Taysiders were relegated two years ago, said: "It means so much to everyone at the club.

"I don't think it will sink in but as a young manager it means the world.

"It is the proudest moment of my career because I have had many sore ones.

"I have failed but I will always dream.

"At the start of the season it was my dream to take this club back into the Premiership and now it is real.

"It is all about the players and to a man they have been unbelievable."