Around 5,000 Everton fans made the trip from Merseyside to witness a frustrating display at Elland Road, as they slipped to a 2-1 defeat.
Heitinga captained the Toffees on his 100th start for the club and understands the supporters' frustrations.
"We need to bounce back, especially for the fans," the 28-year-old told reporters.
"We came with 5,000 Evertonians, which was great. The support of them was really great. It was because of us that we lost, not them.
"The next round when you see Leeds playing it will still be hard that we're not continuing in the cup, but that's football.
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"You need to focus on the next couple of games and we need to bounce back now. Not only for ourselves, but for the fans.
"The confidence is still in the team because we've played really good football over the last couple of months, we're near the top of the league and we want to stay there.
"We are out of the competition now and we need to focus on the league instead. There is not much time to think about this game because the next game is in a few days.
"It was a big disappointment, we started really badly. We didn't play how we normally play and they scored an easy goal in the first couple of minutes.
"After that, the first-half was them. We didn't create anything, there was no spirit.
"In the second-half you could see there was a different kind of way that we played with Felli [Marouane Fellaini] up top behind Victor [Anichebe] and we created some chances.
"The second-half was more of a contest but we lost the game in the first-half.
"We've got a good squad and sometimes you have games like this, it happens. Unfortunately we are out of the cup now and we need to focus on the next game on Saturday."
Everton's next game sees them host Southampton at Goodison Park on Saturday afternoon.