Marlon Harewood's controversial 79th-minute goal cancelled out Michael Bostwick's opener and looked to have earned the Reds a point.
The visitors' hopes were dashed as captain Rowe struck a late winning goal with just two minutes remaining.
He said: "I would have been disappointed with a 1-1 draw so I'm absolutely gutted to end up with nothing.
"The lads fought tooth and nail just as they had been doing for Keith but we just lacked that killer touch in front of goal.
"Our end product is something that has let us down all season but it is something we will continue to work on for as long as I'm here."
Flitcroft was left coy on his own future following the late setback.
He added: "It's a very strange feeling not working beside my best pal as I have been doing for the last six-and-a-half years, but Keith asked me to stay and fight on which is exactly what myself and the players did.
"I'll continue to give everything either as a number one or number two for this football club."