A first-half strike from Christian Ramirez settled the match at Pittodrie, with Aberdeen moving to within four points of their visitors.
Glass has come under pressure following the Dons’ poor run of form and was left satisfied with his team’s result.
"I am relieved,” said Glass. “You take away the opportunity for people to point the finger at ourselves as a group collectively and myself individually, especially the manner in which we dug out the result.
"The main aim is to try and prove people right that support you. Dave was very vocal in his support during the week on behalf of himself and the board but he fronted it up and I want to prove the people right that put me here.
"I want to prove my family right after I made the choice to come back here. It's a big challenge and it's one that I am up for."
It was a resolute display that got Aberdeen over the line with defenders Calvin Ramsay and Declan Gallagher forced off in the first half through injury, potentially leaving them very short for Wednesday’s trip to Rangers.
Scott Brown was forced to drop into the backline but the skipper marshalled the Reds to victory.
Glass added: "We had to reshape the team, throw bodies on and players had to play in positions that are not natural to them so that side of it was part of the win.
"Like recent weeks, I don't think we gave up too many opportunities for the other team to score and if we had made the mistakes that we had previously, maybe I would be sitting here saying the same things again."