The hosts created the better chances and Matt Ritchie came closest to scoring when he hit the bar.
Exeter's best chance came when Ryan Harley was also denied by the crossbar.
"We are the away team so we have to be happy with a point," said Tisdale. "Swindon had lots of chances, especially in the first half, and it was a hard afternoon.
"It was one of those days when you have to dig deep and work hard and be happy with a draw, although I did not say that to the players.
"Both teams were trying to win the game but we have to be pleased with a clean sheet. I was pleased with our effort and commitment and we looked a lot sharper defensively after half-time."