Steve Tully's poor tackle on Billy Bodin led to Rene Howe scoring the only goal of the game from the penalty spot in the 17th minute.
That spot-kick secured the points for the Gulls, who had to withstand plenty of pressure from the home side, but Exeter failed to turn their second-half dominance into goals.
"We paid the price for giving away a very soft penalty," Tisdale said. "We were certainly good enough to create chances - and we did - and I'm left wondering how we didn't score.
"We worked the goalkeeper, we had plenty of corners and opportunities and on the whole, we didn't do too much wrong. We just gave away a very, very poor penalty. It was a foolish piece of defending.
"The first goal is so important here. The players need to release themselves from that anxiety and be pragmatic. If we had scored one, we would have had the chance of a second, so there really wasn't too much wrong.
"The result certainly influences your emotions and if I have a criticism, it is that we didn't play with enough patience in the first half. That was essential.
"We just have to relax a bit and not worry so much. But the reason we lost the game is because we gave a very poor penalty away and that gave Torquay something to defend."
