Steven Gohouri's dramatic stoppage-time equaliser stole a 2-2 draw for Wigan and confirmed Hull's relegation to the Championship.
The Tigers fell behind after half an hour when Victor Moses curled the ball in off the post, his first strike for the Latics since joining from Crystal Palace.
Hull looked to have turned the match around as youngsters Will Atkinson and Cullen also opened their Premier League accounts, but Gohouri - another Wigan first-time scorer - struck with a late acrobatic effort to send the visitors down.
Cullen, who made his first start on Monday, told ESPN: "Obviously we took the lead and had faith in the back four and thought we could keep a clean sheet in the second half but obviously it didn't happen, so it's a big shame.
"The spirit in the dressing room is still high, we're all looking forward to next season now and hopefully we can get back into the Premier League at the first time of asking."
Cullen added: "The future is definitely bright at Hull City. We've just got to keep playing football on the pitch and picking up points if we can."
Wigan manager Roberto Martinez hailed a successful season following their final home game.
He told ESPN: "It's a feeling of a job well done. There have been real highs and lows but there's a fantastic feeling with the fans. It's important we celebrate, we've stayed in the Premier League."
On today's performance, Martinez added: "We were very disappointed with the two goals we conceded but there were many good things and we showed character.
"The players got their reward with that final goal. Hull were very well organised and it was hard to break them down."
Although Wigan's season is effectively over, they could yet have a say in the direction of the Barclays Premier League trophy.
The Latics take on Chelsea on Sunday and, if they take anything away from Stamford Bridge, that would open the door for Manchester United to make it four titles in a row.
"We'll prepare to go to Stamford Bridge and we all know it's going to be a tough game," he said. "We're all excited, we've shown during the season we are capable on the day and we'll work as hard as we can."
Hull boss Iain Dowie admitted it was an unsavoury way to have their relegation confirmed.
"It's a gut-wrenching way to lose what I thought was a deserved three points," he told ESPN.
"It was a spirited display. It's a horrible feeling but these things happen when you're down there."
Dowie added: "Those fans don't deserve to go down but there are a lot of positives."
As for his own future, Dowie said: "It's not up to me, it's a question you have to ask a thousand people. I've enjoyed it, there's a strong spirit amongst the players but it's an unforgiving league."