The Spurs boss was a relieved man after extra-time goals from Roman Pavyluchenko and Jermain Defoe ensured the holders a place in the Wembley final against Manchester United on March 1 after Championship side Burnley overturned a 4-1 first leg deficit to win the second leg 3-0 in 90 minutes at Turf Moor.
However far from being delighted with the 6-4 aggregate success, Redknapp was fuming with some of his players, while he lost several key players to injury problems ahead of Saturday's FA Cup fourth-round trip to Manchester United and Tuesday's Premier League clash against fellow strugglers Stoke.
Defenders Jonathan Woodgate and Michael Dawson also picked up knocks, while Jamie O'Hara suffered a groin strain against the Clarets. And Redknapp admitted that he will have to play the weakest side he can find at Old Trafford.
He said: "It's a hard job I have on here, believe you me.
"I keep saying that we need stronger players in here because we're not mentally or physically strong enough.
"We're in a relegation battle and I can't risk O'Hara, Woodgate and Dawson at Old Trafford in the Cup.
"It's a challenge and it can't get any worse. When I took we had two points from eight games but Stoke is a massive game for us."