He told Sky Sports: "In the first half we didn't really get hold of the ball, and I changed it at half-time.
"They played well in the first half and opened us up and we switched off on a couple of occasions.
"We had to go for broke in the second half. I brought Jermain Defoe on and luckily enough it worked.
"And we took the game to them from the start of the second half, got on the front foot. It was a great second-half performance."
He continued: "We can beat anybody and this win today has put us right back in the race again. It is wide open.
"We can achieve anything. We have to believe. It is not impossible to win the title. Let's see how we go."
Redknapp also hailed the display of Gallas, who left Arsenal at the end of last season and joined North London rivals Spurs in the summer.
He said: "I thought William Gallas was just amazing today. For me, he was the man of the match. I thought his performance was top drawer."