With the visitors leading 10-6 through Roddy Grant's converted try, prop WP Nel fumbled the ball in attack to allow Zebre to surge forward, with centre Giulio Bisegni finishing a neat move under the posts.
Kelly Haimona added the extras to compound Nel's mistake before winger Michele Visentin touched down late on to ensure Edinburgh lost a third consecutive match to Italian opposition for the first time in their history.
And despite the dramatic turnaround that consigned Edinburgh to their fifth GUINNESS PRO12 defeat of the season, Solomons admits his side had enough chances to make the game safe before Zebre's comeback.
"It was a game that I felt we could and should have won, so it's disappointing to say the least," he said.
"I think we struggled in that first half because the penalty count was massive against us.
"We had five penalties against us in the opening nine minutes, so we struggled for territory and possession. To come into the shed at 7-3 up after that, I thought we were in a good position.
"Then they got an 80-metre try on a turnover where WP Nel knocked the ball forward. That was almost a 14-point turnaround.
"We were most unfortunate in this game. Yes, there are areas we can look on, we were heavily penalised in the first half and the scrum did not function well and was penalised a number of times.
"But we should have done better and the players are bitterly disappointed about it."
Click here for the best images from Zebre's triumph over Edinburgh
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