"You think it's not going to happen that they're going to score again, but bang they do and it happens again and we're into extra-time," the Fulham boss said after the game.
"Both fans should be proud of their teams, it was a fantastic game.
"The Everton lads looked devastated at the end and they've put everything in to it so we're happy.
"Inamoto scored a terrific goal and is a gifted player, he's got a fantastic technique. He tired in extra-time but had a really good game.
"It's good to have a home tie next round. Any home draw is a good one and we're confident of getting into the quarter-finals, though West Ham will provide a good game.
"We've had a little bit of luck in the cup so far. We didn't really deserve to beat Cheltenham, but sometimes you get a bit of luck and that's the way it goes."