Mulgrew opened his international account as Scotland secured their first win under Strachan, who was appointed to the role last month.
The Celtic defender converted Charlie Adam's free-kick seven minutes before the break at Pittodrie and Strachan's side went on to secure the victory.
Asked about working under Scotland's new manager, Mulgrew told Sky Sports: "It's been good, been different, some new ideas in there."
He added: "It was difficult conditions...the most important thing was getting the win so we are happy.
"It is good to get that winning spirit - hopefully we can go on and get more wins."
Burke was making his first Scotland appearance since 2006 and he said: "It's been excellent, him (Strachan) and his coaching staff...I've learned so much so it's great to be amongst it all.
"It was excellent, I was happy with my performance - all round the team did well."