Jermain Defoe's third treble of the season clinched the visitors a 3-1 win and a date at Bolton in the fifth round on the weekend of February 13-14.
"These are difficult games," Redknapp said. "I've won and lost these games when you're fancied to win.
"We came to Elland Road - probably the first time for some of my players. The atmosphere the fans created was just incredible.
"This is a massive football club. It's really a Premier League club and it needs to get back where it belongs.
"Leeds are a good side and they'll certainly go up this year and I can see them being back in the Premier League in the next few years."