Spurs needed extra-time to see off the Clarets and Redknapp conceded: "There is a big sense of relief because it looked game over with a few minutes to go.
"I was stood there thinking it could be the most embarrassing night of my football life.
"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.
"I keep saying that we need stronger players in here because we're not mentally or physically strong enough."