The teams will now meet again at White Hart Lane on 24th March for the replay.
“We kept possession well, though we didn’t create enough chances,” said the Tottenham boss.
“Of course we’ll be the happier side. Before we came here we would have taken the draw. This is a difficult place to come.
“Fulham are a difficult team to beat, they just knocked holders Shakhtar Donetsk out of the Europa League. That tells you all you need to know about them.
“They’re well managed and coached and are not easy to play against. A replay gives us a good chance at home and we’re still bang in there.
“At home we’ve got a big chance, but I bet Shakhtar thought they were favourites for the second leg of that Europa League tie.
“It didn’t work out that way, though. Fulham’s win was one of the results of the season.”
Redknapp also hailed Spurs goalkeeper Gomes’s performance in the game.
“Gomes looks different to the goalkeeper who came here in 2008 when I first arrived,” he said.
“He had a terrible time here then but he’s a different lad now, full of confidence, who looks what he is – a top keeper.
“He had a bad day here in 2008 but it didn’t affect him today.”
