Missed bonus point frustrates Solomons
Damien Hoyland scored two tries, while Edinburgh also managed a penalty try, but they couldn't score a fourth try and missed out on a bonus point as a result.
Luke McLean scored the only try for Treviso, who have now lost 23 matches in a row, and were beaten for the first time under new boss Marius Goosen.
But it was Solomons who was left frustrated as his team missed the chance to go second in the Pro12 as they picked up just four points.
"I thought we left the bonus point out there," Solomons told BBC Scotland. "There were three cold opportunities for more tries.
"But, bearing in mind we were coming in after two massive derby games, it was a creditable performance.
"The big thing for us is to make sure we are clinical when it comes to finishing.
"We are creating opportunities, we need to finish them off. I'm pleased with where we are.
"The league is a marathon, it's not a sprint, and there's a long way to go.
"But when I think back to 2013, I'm very pleased with the progress we've made."
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