Edinburgh went into today's match having won just one of their opening five league matches but flipped the form book on its head to record an unlikely win, with Tim Visser scoring the winning try late in the game.
"We know we have got a long way to go. We are under no illusions on that. But to me, it is important that we keep improving week by week. It was great for the guys that they got that result. It was a real boost to their confidence," Solomons told PA.
"Of course, that will help them take their next step up. But what we have been saying is that we need to be performance focused - not result-focused. If we get our performances right, and we have been so close, we will be okay. When we go through the match review on a Monday, we have been saying to the guys you are so close you won't believe it.
"I'm a massive believer that the difference between success and failure is the finest line in the world. If you persevere, you will cross that line. We are a determined lot and we are most certainly going to persevere."
Edinburgh's next match in the Heineken Cup will see them face Perpignan next Sunday.