Treviso's Luke McLean had dotted down to level the scores midway through the second half after full-back Greig Tonks - on his return to the Edinburgh side following hamstring problems - had scored early on.
Greig Laidlaw slammed through ten points from the kicking tee but Solomons believes his side should have made sure their dominance was reflected in the scoreline.
"We had loads of possession, we dominated them for most of the game and we were just frenetic," he said.
"It's probably the most possession we've had all season and it was like we almost had too much possession in a way.
"The error rate was shocking. We must have left at least half-a-dozen opportunities to score tries on the table, so it wasn't a good performance. Because we played at such a frenetic pace, we made a lot of mistakes.
"We did well to come back and score, and the positive thing is that we came back to get the result at the end of the day.
"I suppose if we learn the lesson and get the result it's a good thing."
But perhaps Edinburgh's most concerning development of the night was the loss of Visser 22 minutes in, as the Scotland international was stretchered off in considerable pain.
Solomons added: "(Tim Visser's injury) looks pretty bad but we won't find out for a day or two exactly how serious it is."