Spurs were trailing 1-0 at the interval but went on to win the replay 3-1 and book a place in the semi-finals where they will play Redknapp's former club Portsmouth next month.
"I don't know what anyone could come to Tottenham to boo about because they've seen football this year that has been out of the top drawer," Redknapp said.
"If you want to be entertained, come and watch Tottenham play. You always get people who don't understand the game. You could be playing badly and winning 1-0 and they don't moan.
"They see the scoreboard and react because the team are losing. Ninety-nine per cent of the fans are fantastic; it's only a few idiots.
"It's happening all over the place at the moment. It's happened to Martin O'Neill at Aston Villa in recent games if they haven't been ahead at half-time.
"Whatever we achieve, it has been a great season. We're fourth in the league and in an FA Cup semi-final. The race for fourth is so tight, that any of the four teams could easily finish fourth or seventh. We're just lucky Everton appear to have started their run a bit late in the season.
"Liverpool have great fixtures in the run-in, and they could be favourites to finish fourth even though they're a few points behind us. I can't see them losing too many games in the run-in.
"Manchester City and Villa are in there but we're playing very well and we're in there with a good chance."
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