Fijian scrum-half Nikola Matawalu scored the game's only try in the first-half with an impressive finish in the corner, and four Peter Horne penalties secured the win for a much-changed Warriors side.
The Italians proved to be stubborn competition in tough conditions, and the visitors' cause was not helped when replacement prop Albert Anae saw red late on for a punch.
But Treviso now leave Scotstoun facing a 12-match winless run in all competitions, and Casellato admitted getting their first win on the board would make all the difference for his new-look side.
"We played a good game," he said. "But in the final eight minutes, when we were five points behind, we were not able to manage the game properly.
"I am convinced, as I said after the European game against Racing Metro, that we are missing just one victory which will give us the peace of mind to handle the decisive moments of our games.
"We arrive at the end of the match and it almost seems like we do not believe we can go all the way and win, but a victory will restore our confidence.
"We had a lot of players missing this week who are involved in the Italian side so we decided to be very simple in terms of tactics and it worked for most of that game.
"We chose not to take risks as we knew that they have a good defence, so we set up the set pieces to try and put them in trouble and we did well for at least 72 minutes.
"But right at the end we did not do our job well. We were deep in our own territory and unable to handle the ball properly, so we have also lost the bonus point as we did against Connacht and against Racing Metro.
"The guys definitely deserved something more, and I feel bad for the kids as unfortunately we are still talking about another game without victory."
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