All looked lost when Saints trailed 2-1 at Selhurst Park but they were thrown a lifeline by Danny Higginbotham's injury-time equaliser - his first ever goal for the club.
"Danny's could be an important goal, and what a time to score it," Redknapp said after the game.
"We just threw everyone up at the end and he was there on the spot when the ball dropped to him.
"We gave another bad goal away to fall behind, but even then, we kept going and that was the most important thing.
"I don't know what will happen next week.
"Palace could win, we could win and Norwich could lose.
"All I know is that we will keep going and give it our best."
Striker Peter Crouch was shown a red-card at Selhurst Park and Redknapp was disappointed with the match officials handling of that situation.
"As far as Crouch's sending off was concerned the referee said that both players were going to get yellows and the fourth official got involved and then gave them reds," the Saints boss added.
Crouch will be automatically suspended for the game against United at St Marys next Sunday.