The Brazilian's error against Real Madrid ended Spurs' faint hopes of reaching the Champions League semi-finals.
But his manager has rushed to his defence and backed him to rediscover his form against rivals Arsenal.
Blunder: Heurelho Gomes allowed Cristiano Ronaldo's strike through his grasp
'No chance. I've never ever thought about getting rid of him,' Redknapp told the Daily Mirror.
'I've got no problems with Gomes. He's a fantastic goalie and what he needs now is support. He's made one mistake and he needs support. It's no good people having a go.
'The one thing he doesn't need is what he had when I first got here. He'd make a save and everyone would cheer and stuff. He doesn't need that.
'You need people to realise that he's done a great job here. He's a great goalkeeper and we want him to come out on Wednesday and do what he did last year against Arsenal. He won the game for us.
'He made saves last year that he had no right to make.'
Redknapp is aware that Spurs will have to be active in the transfer market if they are to compete for the title next season.
'I keep saying, this club isn't that far away - if they want to push on - from winning the 'championship,' he said.
'You can't stand still. It means improving. Better players make you a better team. With one or two additions, I think we can go on and push for the title.
'Everyone will go at it in the summer. Arsenal will. Liverpool will - Liverpool are going to be a team to be reckoned with next year.
Wing wizard: Gareth Bale was named PFA Player of the Year
'They've been out of the Champions League, but I don't see that happening again after next season. With Kenny Dalglish there, I think they'll have a real go for it.
'If you want to be a top club, you need top players. There's no other way of doing it. There's no magic formula.'
The Tottenham manager will also be determined to keep hold of his star players, including midfielder Gareth Bale.
And Redknapp refuted suggestions that the Welsh winger has not be consistent enough throughout the season after he was named PFA Player of the Year.
He added: 'I'd say Samir Nasri at Arsenal's gone off.
'He is nowhere near what he was two or three months ago. When he played against England for France he was flying, wasn't he? But over the season Gareth has deserved it for me.
'I would say Luka Modric is unlucky not to be in it, but I'd go for Gareth.
'Over the back end of last season and this season he has deserved it. And I genuinely believe that - not just because I'm Tottenham manager.'
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?Explore more:People: Harry Redknapp, Luka Modric, Kenny Dalglish, Gareth Bale Places: Madrid, Liverpool, France, United Kingdom
Source: Daily Mail
Source: Daily Mail