Palace won after Evann Guessand scored in the 90th minute against 10-man Wolves, lifting them to 13th in the table.
During the game, a protest banner at Selhurst Park read "Opportunities missed - board inept. Fans disrespected - Glasner finished." But the Austrian coach revealed he had received reassurances from Palace's hierarchy about his position.
"I spoke to the board, to the chairman (Steve Parish), to the sporting director (Matt Hobbs) and they said, 'No we think you are the right one'," Glasner told the BBC.
"For me, it's important that they (fans) support the team, and they did it until the end. Of course, the fans are like us all, disappointed with some results and some parts of the game - that's normal."
The fans' opposition to Glasner stemmed from his comments earlier this week when he urged them to "stay humble" after they called for his sacking following a 1-1 draw at Zrinjski Mostar in the Conference League playoffs.
He suggested the critics had lost perspective after guiding Palace to the FA Cup last year, the club's first major trophy in 120 years.
"We had the best two years in Crystal Palace's history and then it's not so easy for a club to say 'Hey, it's better you leave'," he added.
Glasner, 51, said last month that he would leave Palace after his contract ends this season and clarified his position amid speculation about his future.
"I don't know if the club has a different idea, I don't want to stay in the way, and then we will find a solution," he said.
"I didn't say I will step back, I will resign (or) whatever, so maybe now it is clearer."
'Glasner not important'
When pressed about whether he wanted to remain until the end of the season, Glasner said: "Oliver Glasner is not important. Crystal Palace is important.
"If the club had thought they need a change then I don't want to be in the way. That is what I meant."
Glasner revealed he had also spoken with his players about his future, stressing the importance of having their support.
"It's not that I have to live in London because otherwise I don't know what to do," he said.
"No, the most important thing is Crystal Palace, and I am here 100% to be successful for Crystal Palace.
"I need the players... It's important that the players are believing in what we are telling them, I and the staff."
Read the full match report from Palace's win with Flashscore.