However, Redknapp believes that despite Spurs having home advantage in the replay, the tie is far from over.
"We kept possession well, though we didn't create enough chances," the Tottenham boss said after the 0-0 draw at Craven Cottage.
"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."