Late goals from Roman Pavlyuchenko and Jermain Defoe saved Spurs from further embarrassment, but Redknapp knows there is no disguising how poor his side are.
'This is a football club that has been put together by I don't know who, and I don't know how. It's a mishmash of players with people playing where they want to play. It's scary. It was almost the most embarrassing night of my career."
Until Pavlyuchenko's goal in the 118th minute, Burnley were going through on away goals, and Redknapp added: 'There is a big sense of relief because it looked game over with a few minutes to go.
"Burnley played ever so well, they passed the ball well and played with so much enthusiasm, but they didn't have that many chances. It's a hard job I have on here, believe you me.'
Redknapp again criticised his side's fragility, saying: 'We need stronger players in here because we're not mentally or physically strong enough."
Redknapp made six changes from the side which stumbled to a 1-1 home draw against Portsmouth on Sunday, yet none of his players made a favourable impression. Jamie O'Hara, Jonathan Woodgate and Michael Dawson all look set to miss Saturday's FA Cup fourth-round tie at Old Trafford on Saturday.
Redknapp said: "Some key players have got injured tonight and I will go there on Saturday with the weakest team I can possibly find on Saturday. Woodgate and Dawson can't play and O'Hara has done his groin.
"It's a challenge and it can't get any worse. When I took over we had two points from eight games but Stoke is a massive game for us."
Spurs will now face Manchester United in the Carling Cup final at Wembley on March 1.