But the boot of Carlo Canna proved to be Edinburgh's undoing, the fly-half amassing 14 points in all from the kicking tee.
Nathan Fowles kicked two penalties for the Scots but they were held at bay in the final stages by Zebre who claimed their first win of the season and inflicted Solomons' first reversal of the new campaign.
"I am very disappointed with the result, take nothing away from Zebre they played some good rugby and I said during the week that the Italian teams are a different animal at home, but we gifted them chances and let them play," said the Edinburgh head coach.
"In any rugby match if you concede 18 turnover and 14 penalties then you are really going to struggle because that is 32 times you are effectively given the opposition the ball and that eventually takes it out of you and leads to points being conceded.
"I have praised the guys a lot this season for the way they have been playing, but in this match nothing seemed to be going our way and things just did not click.
"In the last few minutes we have it a really good go and credit must be given to Zebre's defending, but we did not have the cutting edge needed."
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