Pat Lam's team trailed throughout the contest, yet stole the points with a last-gasp try from Willie Faloon sealing a 14-13 victory.
And Solomons, whose team profited from a one-point victory of their own against Munster last week, is determined to shake up his pack and avoid a repeat of Friday night's surrender.
"The set scrum was difficult," said the Edinburgh coach.
"We will sit down and go through every one of them with a fine toothcomb. We have to get to the bottom of it because that was a killer for us, even right at the end there.
"I thought that the scrum made an enormous difference. We were just too passive, we were too flat, but there is no doubt that what happened at scrum time had a bearing.
"We spoke all week about how we peaked against Munster and we spoke about making sure that we were in the right frame of mind, mentally and physically.
"We took things relatively easy during the week and, obviously, Connacht are a side never to be underestimated. We just weren't at the races."
Victory for Connacht kept their 100 per cent winning start to the season intact, following last weekend's triumph over Newport Gwent Dragons.
Yet coach Lam admitted the way the match played out had taken its toll on his players, even though they snatched victory from the jaws of defeat.
"It's quite a sombre dressing room," said Lam. "Again, we're pleased with the win but very frustrated with handling errors, dropped balls and lack of execution.
"We made a lot of mistakes but thankfully we kept the pressure on to grind out the win.
"It's back to work on Monday for a massive week ahead of the game against Leinster."
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