The majority of the Ibrox crowd held up blue cards, distributed beforehand by The Union of Fans, on 18 and 72 minutes to back reinvestment by the former director, who lost £20million when Rangers went into liquidation in 2012.
The South Africa-based businessman has expressed concerns about the club's finances and is in Glasgow for talks with the board and fans groups.
McCoist has made it clear he is no longer willing to discuss off-field issues and, when asked for his thoughts on the fans' actions, he said: "I would congratulate and thank them for their support. That's all I would say.
"Their support has been fantastic throughout the season. Of course, you would need to have your eyes shut not to see the blue card protest on 18 and 72 minutes but that's not for me to comment on, other than thanking them for their support.
"I haven't spoken to anybody from the board at all regarding their meeting but I don't have any doubt that Graham (Wallace, chief executive) and I will have a chat. I would imagine that would be one of the topics of conversation."
Events behind the scenes did not prevent the newly-crowned champions doing their job on the park.
McCoist added: "It didn't at all and that's really encouraging because the players have been totally focused this season on getting results and that has to be the case.
"It's always our job to make sure the players and staff are focused on getting results because that's the only thing we can have an affect on. We will continue to do that."
Steven Smith opened the scoring with a fantastic free-kick, before youth player Callum Gallagher marked his debut with a last-minute strike.
McCoist said: "I thought the first goal was a bit special. We had been going over free-kicks on Friday and even on the morning of the game and none of the rehearsals featured that one to be honest.
"It was very taken and well-received by our dug-out. It was a great strike.
"Young Callum also did well. We have been enjoying his progress with the under-20s and he is one of the lads who has been performing at a good level all season.
"He deserved his chance and he took it. For him to come on and score was a dream for him and I'm delighted for him because he's a great kid."
Rangers now turn their focus to Monday's William Hill Scottish Cup replay against Albion Rovers, with the winners facing Dundee United in the last four at Ibrox.
According to reports on Saturday, the Scottish Football Association has rejected United's request to move the semi-final to a neutral venue if Rangers are the opponents.
McCoist said: "That's obviously a decision that I won't have anything to do with, so we will just have to wait and see."
Dunfermline boss Jim Jefferies, who saw Danny Grainger sent-off with 12 minutes to go, insists his side deserved at least a share of the points.
And he felt Ross Forbes, booked shortly before Rangers' opener for diving, should have had a penalty instead of a caution.
Jefferies said: "Maybe somewhere else we might get it but I thought it was a penalty. I thought it was a harsh decision and it might have made all the difference.
"I don't think the scoreline was a fair reflection of the game. If anything, we had more of the possession than Rangers and we defended very well. But they showed us how to be clinical."