There were no tries in the clash that took place in miserable conditions at Murrayfield as Stephen Ferris made his first start for Ulster after 16 months out with injury.
Defeat ends Edinburgh's run of four wins in their last five league games but Solomons could at least take solace from how close his current outfit ran his former employers.
"There was nothing in the game between the sides - the penalty count was pivotal," he said.
"They scored two penalties from scrums. Neither side scored a try, there were just two penalties in it and that had a major bearing on the game.
"Ulster are very powerful - they are amongst the top three sides in Europe. They've been together for a long time."