Dortmund held a two-point lead atop the table before the final round but were held 2-2 at home by Mainz, allowing Bayern, who won 2-1 at Cologne, to jump up to first place, winning the title on goal difference.
Terzic was seen in front of the club's famous yellow wall after the final whistle in tears, as the fans chanted the Dortmund-born coach's name.
"You can see how hard and how tough this sport that we fell in love with can be," Terzic said, adding "it hurts extremely - there will be no happy ending for us this year."
Dortmund won the unlikely support of Bayern captain Thomas Muller, who took time out from celebrating his side's 11th straight title - and his 12th Bundesliga championship - to express sympathy.
"I'm not apologising for becoming champions and we're happy about that, but when you think of the others, then I feel a bit sorry.
"Even if they don't want or need to hear it. I'm not trying to present myself as big hearted or anything, but it's tough."
Captain Mats Hummels, the only member of the squad to have tasted championship glory with Dortmund said "the next days will be brutal.
"It's going to be difficult to digest. It will take more than a few days."
Dortmund midfielder Emre Can said simply: "We gave everything as a team but it wasn't to be."
"We wanted it but in the end we didn't make it."
Dortmund led the table four times this season, but each time dropped points and allowed Bayern to return to the summit.
