The Scarlets stormed back to lead 18-13 at half-time with full-back Jordan Williams scoring two tries, but when Tom Brown went over on 45 minutes, Edinburgh were level again.
Scarlets centre Adam Warren's try proved decisive however and having lost 9-7 away to Connacht in their previous match, Solomons admitted Edinburgh's away form must improve.
"I think we have ourselves to blame again, for not winning the [Scarlets] game," he said.
"Our error rate was high and the consequences were that, every time we got an opportunity to attack, we made a mistake; lineout malfunctions and isolated, single-man runners. It cost us the game.
"The effort was certainly there from everyone in the team but the mistakes caused us problems.
"We've shown that we've got enough about us, providing we cut our error rate, to get results like this one on the road.
"The disappointing thing is that we should have got a win but we blew it with errors.
"We're certainly disappointed with our last two games.
"They are matches we could and should have won, but we need to put that right and are looking forward to the opportunity to do that against Ospreys."
Follow us on Facebook, join the conversation on Twitter, sign up to ourYouTube channel for extensive match highlights and sign up to our newsletterfor regular updates on the RaboDirect PRO12
63x46.png){kind=logo}