Jonathan Woodgate's late header clinched the victory at the KC Stadium which moves Spurs five points away from the relegation zone.
But Spurs must now play Shakhtar Donetsk in the second leg of the last 32 of the Uefa Cup on Thursday before meeting Manchester United in the Carling Cup final on Sunday.
Redknapp is set to rest key players again for the Shakhtar clash and is unhappy at having to play so close to the club's Wembley appearance.
Crazy"I hear people criticising that I have rested players, but tonight was the all-important game," said Redknapp.
"Whoever heard of you playing Thursday night before playing a cup final at the weekend?
"People have been in cup finals over the years, you don't play Thursday night. You go away for two or three days and have a rest.
"The whole fixture list is crazy."
Redknapp was pleased with the win over the Tigers and believes his team's second-half performance ensured Spurs deserved all three points.
DifficultHe added: "If they'd have won I think they'd have been out of it, but it's kept them in it.
"We're back in the pack again and that's important.
"It was always going to be difficult. They are difficult to play against. They have played a direct game and were dangerous on set plays.
"I thought second half we got the ball down and passed it and we were much the better team."
Match-winner Woodgate suffered a head injury in the closing moments, but Redknapp is confident the defender will be fit to face United at the weekend.
The Spurs continued: "He's a tough nut, I don't see him not playing at Wembley."