"It was a great result for us on the back of a big down on Sunday," he said.
"It knocked us all for six. So to play like that after Sunday is fantastic."
Redknapp also praised the Spurs fans who acted like an extra player on the night.
"The crowd want to beat Arsenal more than anybody," Redknapp added. "They were right with us tonight.
"We hung in there late on and the keeper made some fantastic saves. He was superb tonight.
"Everybody worked hard and it was a great result.
"They started well and kept the ball but it was only late in the game the keeper came to our rescue. They had a lot of the ball but they had few clear-cut chances."