Edinburgh were impressive in winning 27-16, but the lack of an extra clinical edge saw them miss out on a fourth try.
They failed to capitalise on numerous gilt-edged opportunities towards the end of the tie.
The home side went into the break 13-6 up courtesy of a solo try from winger Tom Brown, converted by Greig Laidlaw, who also added two penalties. Perpignan's reply came in the form of two successful penalties from James Hook.
A Hook effort early in the second half drew his side closer, but the sin-binning of visiting captain Guilhem Guirado proved pivotal, as Edinburgh made the most of their numerical advantage to cross the whitewash on two occasions.
First, flanker Cornell Du Preez barged over from close range, before Tom Brown touched down after a kick ahead from debutant Carl Bezuidenhout.
Laidlaw added both conversions, but his side failed to grab a bonus point, despite overwhelming pressure in the final period.
Perpignan had the final say, with a late touchdown from Maxime Delonca, converted by Hook, rounding off the scoring.
Yet Solomons was distinctly upbeat in his post-match summary.
"I thought we played well," he said. "That was a really good performance by the team. It was a tremendous defensive effort but overall a really good performance and we deserved the result.
"I thought maybe in the opening 20-25 minutes we were making the tackles but we weren't stopping momentum and we had a high error rate. But I thought we built into it and once we got our rhythm defensively I thought they found it very difficult to score."
With regards to the elusive bonus point, Solomons was diplomatic.
"I don't think frustrated is the word. Everybody is a little bit disappointed," he said.
"We had three opportunities to get the try. We went for it. Unfortunately, on the night we didn't get it but I don't think we should let it detract in any way from what was an outstanding performance."
Despite the fact a bonus point was necessary to further their Heineken Cup ambitions, Solomons insisted that they would treat their visit to Munster next weekend as a crucial tie.
"We approach it like we approach each game. We look to try to improve each game, we look to rise to the challenge each game and we look to put in a good performance each game," Solomons said.