But Edinburgh - who started off the GUINNESS PRO12 season with four wins on the trot but have now lost four of their last five - fought back well, Jack Cuthbert going over for the visitors.
And Solomons - who last week signed a new deal tying him to the Scottish capital club until 2017 - admitted his side had to be pleased with a losing bonus point.
"The guys stuck in really well in hugely difficult conditions," he said.
"We gave away a couple of soft tries early on but then we put in a decent defensive shift.
"We had a real chance following our score after half time.
"However, Ulster came back really strongly at us. In many ways a point was a reasonable reward for our efforts."
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