Midfielder Conway put Malky Mackay's side ahead with only his second goal of the season in the 27th minute, but David Edgar's injury-time header earned the Clarets a point.
Conway said: "Obviously we got promoted on Tuesday and went out and had a night out after that so we've had to refocus and we wanted to go and win the league so I'm glad we've gone and done that.
"It's unbelievable. It's been a long season but it's great to win it with two games to spare.
"The manager said we deserve it and to remember days like this as a lot of people go through their careers without winning anything.
"We are lucky enough to be part of it. It means so much to everyone to be a part of it."
Defender McNaughton added: "We've come so close before and to take that extra step it's great to see. Basically I'm just chuffed for the fans.
"It's been a bit like climbing Mount Everest to get up for it and to get that point.
"I thought the boys played quite well today considering the celebrations during the week and we got ourselves back up for that and got the job done."