Bale, who scored a penalty to equalise and hit a late winner, said that the players have put right the defeat to Serbia in their last game.
"We all knew it was a massive game for us," Bale said. "We let ourselves and the nation down [when we lost 6-1] against Serbia, and we wanted to put things right.
"We fought back like men tonight and got a great result."
Wales's victory moved them above Scotland after three games.