The match looked to be heading to extra-time after Dortmund midfielder IIkay Gundogan's 67-minute penalty had cancelled out Mario Mandzukic's opener on the hour.
But Arjen Robben latched on to Ribery's backheel in the 89th minute before cutely rolling the ball into the net to snatch a 2-1 win, to the despair of the travelling Dortmund support.
While Klopp was clearly disappointed, he refused to speculate whether that was the fate his charges deserved.
"First and foremost, congratulations to Bayern Munich because they won so it's not important to speak about what happened in the game," he told ITV1.
"After the game you have to respect the result and that's what we do now."
Klopp admitted Dortmund were visibly fatigued in the closing stages and that may have proved to be their downfall.
Nevertheless, the former Mainz coach paid tribute to his side for reaching European football's showpiece event.
"I didn't see (Robben's) goal. It was a free-kick and we were not in the right formation at that moment. It was late in the game and it has been a really hard season for us," he added
"I saw it from 75 minutes on, it was hard for us. Bayern Munich had to fight too.
"We deserved to be in the final and we showed this tonight and the most important thing but it's important."
Dortmund defender Mats Hummels, like his manager Klopp, was quick to pay tribute to Bayern and admitted they deserved the win as a result of their dominant second-half showing.
The 24-year-old also lamented his side failing to take advantage in the early stages of the game, with Bayern goalkeeper Manuel Neuer having to make several fine saves in the opening 25 minutes.
"The game was really close but in the end it was kind of deserved for Bayern because they were the better team in the second half but for us it's very hard and disappointing," Hummels told Sky Sports 1.
"It's one of the hardest games you can lose.
"I think in the first 25 minutes we were the better team but missed the goals we needed.
"Second half, Bayern got control in the game because we lost a little bit of control when we had the ball. We lost it too early, we didn't have the possession that we needed to get a little bit of pressure."