Paul Scholes' injury-time header gave United a 1-0 win at Eastlands to leave City sweating on securing fourth in the Premier League with just four games to go.
Bridge admitted they were gutted at the narrow defeat but vowed not to give up on the race to qualify for next season's Champions League.
"Losing like we did was agonising, especially as we didn't deserve to be beaten like that," Bridge told the club's website.
"I thought we deserved more than we got, even more than the draw that we nearly had.
"Losing was a real kick in the teeth but the prize is still there. The momentum is perhaps with Spurs but at the same time we know that fourth place is still in our hands," he added.
"We will be working even harder to make sure that we are in the top four come the end of the season."