Lee Jones and Taqele Naiyaravoro touched down for Glasgow, but Black's effort - allied by the combined kicking of Paddy Jackson and Ruan Pienaar - secured a 13-10 win for the hosts.
It was another tense Friday night victory at the Kingspan Stadium following on from the nail-biter with Newport Gwent Dragons in Round 13.
And Barakat insists that Ulster's 'ugly' displays will catch up with them sooner rather than later unless they improve.
"You're winning ugly but if you don't fix it up the bubble will burst," he said. "We've got some important games to play and we're annoyed that we're leaving bonus points out there.
"We spoke last week (against the Dragons) about not playing so well but coming away with the spoils and we repeated that again.
"I thought we had opportunities in that first-half to finish this game and even go on and pick up that bonus point, but it didn't occur and we didn't have the patience, the decision makers, or the skill levels, to finish it.
"It's still positive and we've got to remain positive as we're still leading the competition."
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Guinness PRO12 Ulster News
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