Now sitting third from bottom in the GUINNESS PRO12, Edinburgh are without a win since round one's narrow victory over Munster.
Edinburgh had looked to be coming back into the game in the opening stages of the second period, after a converted Andrew Trimble try and two Paddy Jackson penalties had given the hosts a 13-0 half-time lead.
But skipper Mike Coman saw yellow on the hour mark and the flood-gates opened, with Nick Williams, Rory Best, and Trimble all going over before the end to give Ulster the bonus-point victory.
Head coach Solomons admitted his side shot themselves in the foot with penalties, but also believes the number of Edinburgh's absentees through injury has had a significant impact on their form.
"You have to keep the game in context and keep a perspective on things," Solomons told the BBC. "Ulster are very strong.
"The turning point in that game was the yellow card that was given and the succession of mauls that took place straight after that, which led to two tries - I think then the game has gone.
"So I think the yellow card was a massive thing and the penalty count was a massive thing.
"It makes it very difficult to play when you are on the back end of a big penalty count like that, especially against a very strong side.
"We missed a number of key players who could not play because of player management issues.
"Dave Denton didn't play, Matt Scott didn't play, Dougie Fife didn't play and Grant Gilchrist went off at half-time.
"When we play these top teams, especially in away fixtures, it's important that we have our key major international players playing for us."
Click here for the best images from Edinburgh's 30-0 loss to Ulster.
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