Solomons' Edinburgh have now lost their last four fixtures in all competitions, but did manage the first try of the match through prop Allan Dell.
Edinburgh were 13-6 ahead minutes before half-time, but the Welsh side levelled with a try before the break and dominated from that point onwards.
"The biggest factor was discipline," said head coach Solomons.
"We talked about it at half-time.
"We said we have dominated possession and territory, we've got to keep doing that, but our discipline wasn't good.
"I thought we played really well in the first half. We had possession and territory and missed two kicks at the posts that perhaps we should have got, then they got a very good try.
"So, after dominating territory and possession, right at the death, we go in 13-13.
"The second half was the reverse. They dominated territory and possession and, ultimately, when Neil Cochrane went off with a yellow card that killed us.
"We gave away a lot of penalties, plus a yellow card, and I think that was the difference in the second half."
The defeat leaves Edinburgh fifth in the GUINNESS PRO12 table with all the teams above them having played fewer games.
"We are looking forward to being back to BT Murrayfield. We've been on the road a lot and the last three games have been away from home," added Solomons.
"It is always a difficult period for all the clubs - not just us - over the Six Nations period, but we've got to put in two big performances before we go into the break."
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