Carlo Canna's consistency from the tee and some dogged defending had put Zebre 12-0 ahead, but Ross Ford and Murray McCallum rumbled over in the last half an hour to give Edinburgh the edge.
But Venditti's effort broke a three-game winning run for the hosts, and Hodge believes they had thrown a fourth away at BT Murrayfield.
"Lots of things went wrong, probably discipline was the main thing," he said. "We gave away far too many penalties that gave them a foothold in the game.
"Little bits of set-piece, errors in attack and then - at the end - some real naivety to give them the game. It was hugely disappointing.
"We just couldn't finish things off. There was some good build up play and then a mistake would let them off the hook. That was the story of the night.
"There weren't really any positives to take from the game. The only positive will come if we learn from it and put it into action next Friday night.
"Ulster are obviously a quality side packed with good players. We'll be back at home and will have to take this one on the chin and pitch up on Monday ready to prepare for winning a game on Friday night."
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