Strachan was delighted to collect his fourth trophy out of a possible six in the two seasons he's been in the hot-seat at Celtic Park but felt his side took a while to get into the game.
"We didn't play well in the first half," he said, "especially the full-backs, but we got better and I think most people who saw the game would have said Celtic created the better chances.
But the Celtic manager took time to pay tribute to Stephen Kenny's recently relegated side who expended plenty of effort but lacked a cutting edge.
Strachan said: "I'm not a gambling man but I'd put money on Dunfermline coming straight back up (to the Scottish Premier League) next season."
As he watched his players frolicking on the Hampden pitch after the presentation of Celtic's 34th Scottish Cup, Strachan said: "It's great fun watching people enjoy themselves.
"I used to love this as a player but we never used to have the ticker-tape!"
Celtic defender Steven Pressley became the first player to win the Scottish Cup with three different teams.
"I'm delighted with that," he said, after his previous triumphs with Rangers and Hearts.
"It's an honour to hold such an achievement and something to tell my children and my grandchildren.
"It certainly wasn't a classic in terms of cup finals. We never really got going but again we showed our true resilience.
"It's a fantastic result and I think it's a very fitting end for Neil Lennon.
"He has had a remarkable career at Celtic Park."
Like Pressley, Celtic midfielder Paul Hartley won the tournament with Hearts last season.
And the Scotland international was equally delighted with his day at Hampden.
"A Double in my first season at Celtic...it doesn't get any better," he said.
"I just want more success now, more silverware, it's why I came here.
"It was a fantastic season but it would only have been fantastic if we won today and we managed to do that so we've got to build on this now."