"I've been around long enough to know what to expect," Redknapp said. "I have managed teams in the lower divisions and seen Premier League teams knocked out.
"Stevenage are a difficult team to play and worked their socks off. The pitch was bumpy and the ball was bobbling everywhere - but they are a good side, bang in form."
Liverpool romped into the last eight with a 6-1 hammering of Championship side Brighton, who contributed with three own goals.
Kazenga LuaLua equalised Martin Sktrel's early opener for Liverpool and it was 1-1 until just before halftime when Liam Bridcutt inadvertently diverted Sam Vokes' clearance into his own net.
Andy Carroll made it 3-1 with a nice finish after a slick move and Bridcutt was unlucky again as he turned in Steven Gerrard's shot.
Lewis Dunk then scored a third own goal for Brighton and though Luis Suarez missed a penalty, the Uruguayan headed a late sixth.
Liverpool will play Stoke in the last eight after Tony Pulis' side survived the early sending-off of Rory Delap to win 2-0 at Crawley Town.
Delap was red-carded for a foul on David Hunt but a penalty by Jon Walters and a header from Peter Crouch were enough to see the Premier League side through.
League Two side Crawley began well and hit the woodwork but despite the one-man disadvantage, Stoke took control and ran out convincing winners.
Stoke were then drawn to visit Liverpool in the quarter-finals set for March 17 and 18.
The other games are Everton v Sunderland, Tottenham or Stevenage v Bolton and Birmingham or Chelsea v Leicester.
- AAP