Portugal were overwhelming favourites to triumph in Aveiro, but were undone by Bekim Balaj's superb second-half volley as the underdogs celebrated a famous victory.
The hosts piled on the pressure in search of an equaliser and substitute Ricardo Horta went closest when he thundered an effort against the crossbar late in the game.
However, Albania held firm, and Portugal were met with a chorus of boos from disgruntled fans, with some reportedly waving white tissues in protest.
Bento's position will now come under further scrutiny after Portugal's group-stage exit at the World Cup earlier this year, but he shrugged off the discontent among the Portugal faithful.
"[The white tissues] are normal situations of football," he told RTP. "I think we must respect the choices and decisions of the people and try to continue.
"We know that the game didn't go our way, although I think the result was unfair."
Bento felt his side paid the price for not making the most of a first half in which Portugal largely dominated proceedings.
He added: "It was a game that didn't go well in terms of the result, of course, but in the first half we had opportunities to score. We had the game completely controlled during the first 45 minutes."
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