Duarte also lambasted Angola's "anti-football" saying they had spent the last 20 minutes of the match time-wasting, prompting the referee to add on eight minutes of injury-time.
Mateus and Manucho scored in the second half for the Angolans either side of a superb equaliser by Alain Traore.
Burkina were badly let down by their defence as their forwards created more than enough chances to win the game.
With Ivory Coast, 1-0 winners over Sudan earlier in the day, strong favourites to go through, the match was seen as a key battle in the race for second place in Group B, with Sudan considered rank outsiders.
"Their goals both came from schoolboy mistakes in our defence and we paid for them," said the Portuguese.
"After the second goal, Angola played anti-football which the referee permitted. Obviously teams want to win and will do all they can, but it was ridiculous. They kept going down and wasting time and the referee did nothing."
The first half, while far from a classic, produced half- chances for both sides with Angola, backed by a lively band featuring out-of-key trumpets, looking slightly more dangerous.
The game burst into life three minutes after the break when a sequence of mistakes in the Burkina area ended with Hamadou Tall losing possession to Mateus who cut inside and fired a left-foot shot past Daouda Diakite.
Burkina conjured up a superb equaliser 10 minutes later when French-based midfielder Alain Traore curled a 25-metre free-kick around the wall that left Carlos Fernandes stranded.
The goal brought the Stallions to life and they looked capable of winning the match until the defence lost possession again. This time, Manucho benefited and the Real Valladolid player fired a left-foot shot past the stunned Diakite from outside the area.
Burkina were far from finished and Beli Moumouni Dagano should have equalised when he was allowed a free header from close range but his effort went straight to a grateful Carlos Fernandes.
Dagano was denied again by the goalkeeper as Angola, who resorted to blatant time-wasting, were forced to defend desperately
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