Matt Tubbs grabbed the only goal of the game six minutes before half-time at Plainmoor and the Blue Square Bet Premier side could have had more, but Gulls goalkeeper Scott Bevan saved second-half penalties from Tubbs and Craig McAllister.
Both sides finished with 10 men after Chris Zebroski was shown a second yellow card for handball - the incident that resulted in Crawley's first penalty - and Dean Howell was dismissed for the visitors seven minutes from the end.
Buckle said: "We are disappointed, it's never easy when you lose a game.
"It was a big game for both sides. We weren't at our best, I'll hold my hands up and say that, although it was an unbelievable game with all the incidents, especially the second half.
"We have had lots of good days at Plainmoor but this is not a good day for us."