Sam Hidalgo-Clyne and Roddy Grant praised the leadership of Alan Solomons after in the European Challenge Cup final.
The Scots went down 19-13 but were unable to make their one-man advantage count in the closing stages.
"Alan Solomons has done brilliantly in the last couple of years, he has really moved the club forward," said Hidalgo-Clyne of the South African head coach.
And back-row Grant added: "He's the man to take the club forward."
Solomons, 64, is nearing the end of his two-year contract at Murrayfield and is now enjoying the fruits of his work at Edinburgh.
The match against Gloucester was the first time a Scottish team had contested a European final. Furthermore, with two games to go in the Pro12, his seventh-placed team are knocking on the door of a top-six finish and a place in next season's European Champions Cup.
"We'll wait to see. I'd very much like to be here next season," he told BBC Scotland when asked about an extended stay.
Grant, who described the defeat as "pretty heartbreaking", was in no doubt about who should be in charge of the team next season.
He said: "He's the man, he really is. I can't speak highly enough about him.
"He's brought the squad so tight, he's recruited a lot of great guys and it's the best place Edinburgh has been since I've been there.
"We're playing good stuff. We got so close tonight."
Edinburgh trailed 13-6 at half-time, with Billy Twelvetrees going over for the English side's opening try and Hidalgo-Clyne and Greig Laidlaw exchanging penalties.
Scotland captain Laidlaw kicked another two penalties before Gloucester were reduced to 14 men when Bill Meakes was red-carded for a high tackle with 17 minutes left.
Hooker Ross Ford touched down for a try and Edinburgh forced Gloucester deep into their own half but could not register another score.
"The guys are gutted," said Hidalgo-Clyne.
"Gloucester took their opportunities. We did well to stay in the game in the first half but we didn't take our opportunities in the second half when they got that red card.
"We got into their 22 and then they got a turnover and from there it was game over, really.
"I think we weren't clinical enough."
Solomons added: "We perhaps left ourselves too much to do at 19-6 but I thought at 19-13 we were back in it.
"They looked to be struggling. We were deep in attack inside their 22 and we gave away a penalty at the breakdown and that was really the end of the game.
"It's hard; it's little things that make the difference in finals.
"We gave away the penalty, they kicked to the line, they drove and got another penalty, got into our half and held on to the ball for the last five minutes.
"Fair play to them. That penalty was unfortunately just one of those things.
"This side has got tremendous resilience, tremendous heart.
"It wasn't our night; well done to Gloucester."