Bangladesh did well to restrict India to 105 but their batting collapsed spectacularly, folding up for 58 runs after being wrecked by Stuart Binny's sensational bowling.
"I don't have an explanation for this defeat," Mushfiqur said.
"All I can say is that we had a very good opportunity. There cannot be anything more shameful, so I apologise to the nation on behalf of the team.
"A lot of problems can be identified after such a defeat. Maybe we are trying hard, but I don't know what is exactly going wrong. We will discuss our problems tomorrow, but I think if this were our second team, they would have played better cricket. It is very disappointing," he added.
Mushfiqur rued the shambolic batting by his teammates.
"There can be a lot of questions. We were set in the crease but we couldn't finish the game," Mushfiqur said.
"We had to try as hard as we usually do but our batsmen didn't show the mental toughness required in the middle. When they bowled two or three good overs, we played the wrong shots, which caused the defeat."
The skipper, however, praised debutant pacer Taskin Ahmed, who became the first Bangladesh bowler to grab a five-wicket haul on debut.
"Mithun and I were batting quite well too, but I don't know what happened all of a sudden. Nothing can be worse than this and I didn't expect such poor cricket."
Mushfiqur also expressed his disappointment at Tamim Iqbal's continued run of poor form with the bat.
"Maybe it was his plan to play attacking, but he should have judged the wicket. A 30 or 40 from him would have made a difference but as I said, the approach may be good but the application is not there," Mushfiqur said.
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