Lawrence Shankland gave Hearts the lead from the penalty spot midway through the first half of their Europa League play-off first leg against Zurich but the hosts were ahead inside 12 minutes.
Hearts survived some scares to take a 2-1 deficit back to Edinburgh and Neilson believes their fans can roar them to victory at Tynecastle next week. "I thought the players were outstanding," he told Hearts TV. "We started the game well and got the goal, and then lost two goals in quick succession which rocked us a wee bit.
But I thought the players responded really well. "To come here against the Swiss champions, with a lot of international players, a very, very good team, and we held our own, created chances.
Yes, at times we rode our luck, but that's part of football. "I was really pleased with the players but now we have a chance when we go back to Tynecastle next Thursday, 20,000 fans screaming their head off.