The Toffees lost 2-1 in the third round of the Capital One Cup at Elland Road with the Dutch defender vehemently apologising to the 5,000 travelling supporters.
"We need to bounce back, especially for the fans," said Heitinga.
"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.
"You need to focus on the next couple of games and we need to bounce back now. Not only for ourselves, for the fans.
"The confidence is still in the team because we've played really good football the last couple of months, we're near the top of the league and we want to stay there."