The Welshman's goal levelled the match after Spurs had been 2-0 down, but Mario Balotelli's injury-time penalty earned City a dramatic win.
"Everyone's devastated," Bale told the club's official website. "We can take heart from the performance, but we all feel sick that we've lost the game that way.
"I don't think we deserved to lose the game.
"We showed our character to come from 2-0 down and I thought we should have won the game. We can't quite believe it."
The defeat has left Harry Redknapp's side eight points off Premier League leaders City.