Bayern Munich won the DFB-Pokal 2-0 in extra time in Berlin on Saturday but Dortmund probably should have been awarded a goal just after the hour mark when Hummels got on the end of Nuri Sahin's free-kick.
While Dante cleared the ball away for Bayern, replays showed the ball was clearly over the line before the Brazilian defender got his foot to the ball, although there was also a suggestion that Hummels was offside.
After a scoreless 90 minutes, Bayern triumphed in extra time thanks to goals from Arjen Robben and Thomas Muller.
Klopp, who had declared before Saturday's match that the German Cup had been his main priority throughout the season, was clearly disappointed to have missed out at the Olympiastadion.
"It's a painful defeat because it's a big competition. Both teams pushed each other to the limit today," the 46-year-old said.
"We had a good goal disallowed and that was a shame. We were going well at that stage."
While Dortmund's coach seemed philosophical about both the referee and the assistant failing to spot Hummels' header going over the line, he made it clear he considered the 64th minute to have been a turning point.
"There were few games where a goal would've done us more good than that one," Klopp said.
Bayern claimed a domestic double with their triumph in Germany's capital, while Dortmund finished the season with just the German Super Cup for silverware.
And although Klopp claimed it was still 'an exceptional season' for his team, Dortmund goalkeeper and match-day captain Roman Weidenfeller argued his team 'deserved more' on Saturday.
"Everyone's very disappointed," Weidenfeller said.
"We deserved more from the match but it wasn't to be.
"As usual, the little things were what decided a match like that."
