The Brazilian's error cost Spurs a goal against Chelsea last week - although replays showed Frank Lampard's shot did not actually cross the line - and he also fumbled a Cristiano Ronaldo strike to give Real Madrid a 1-0 win at White Hart Lane last month.
But Redknapp urged supporters not to mock Gomes with 'ironic cheers', which they have done before this season, and asked them to give the goalkeeper a positive reception when Spurs take on Blackpool.
Close call: Tottenham's goalkeeper Heurelho Gomes stops Frank Lampard's shot on the line
The Tottenham boss said: 'He's made a couple of mistakes, but it's up to Gomes now to come through that.
'It's up to him to come out and have a great game and play well. You need the crowd to support him now, you need everybody.
'What I don't want to hear is - when he makes his first save - ironic cheers or something. It doesn't help the boy's confidence and it doesn't help the team. It doesn't help any of us.
Blunder: Gomes fumbled Cristiano Ronaldo's shot into his own net against Real Madrid
'We need them, like they did with Crouchie (Peter Crouch) - the fans were fantastic with Crouchie, after he got sent off (against Real Madrid).
'The fans have been good here. They are good. I've got nothing to criticise them about.
But, just to say, a lot of it is fun but it doesn't help, and hopefully it won't happen tomorrow. It doesn't help us. It makes everybody edgy.
'Gomes is a great character, he's a lovely man, a fantastic fella. He's a top goalkeeper. We need everybody to stick with him now, not just suddenly turn on him.'
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Source: Daily Mail
Source: Daily Mail