Tries from John Andress and Phil Burleigh, plus eight points from the boot of Greig Tonks was enough to earn Edinburgh a 20-9 victory.
"We've won three of our competitive games on the bounce and winning generates confidence," Solomons said.
"On Friday we didn't have our best game but we got the win and that's important.
"There wasn't much rugby in the first half. I didn't think they'd kick so much, because normally they play. They kicked the cover off the ball and we made mistakes and gave away penalties.
"We turned it around in the second half and got the win but it wasn't pretty.
"You've always got to give credit to your opposition. I thought Ospreys defended well. The second half was pleasing because we turned it around in terms of territory and possession and we were well on top."
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