His side finished seventh in the regular season but fell short in the quarterfinals, losing 42-33 to a resilient Bulls team at Loftus Versfeld.
The South African-born coach praised his players for their determination to reach the knockouts.
"There was a lot of fight shown throughout this challenging season. We had a tough start against Leinster, we staggered along, but our performances were relatively consistent despite the fact that some results didn't go our way.
"To qualify for a URC quarterfinal is a momentous achievement, and the effort of the team must be commended," said Edinburgh's coach.
The quarterfinal defeat also marked the final appearance for several Edinburgh stalwarts. Jamie Ritchie, Ali Price, Mark Bennett, Javan Sebastian, and Robin Hislop are all departing the club.
Despite the changes, Everitt says he’s excited about the future and was encouraged by what he saw in the team’s performance at Loftus.
"We've cultivated a great environment, and the players are proud to represent Edinburgh. We saw that against the Bulls, I know we fell short, but those are the positives we can extract.
"There has also been a lot of growth that has taken shape over the season, so you can't look at the Bulls game in isolation, and we are certainly excited about what we can bring next season," said a proud Sean Everitt.
Everitt is confident that Edinburgh’s incoming players can help build on this season’s progress.
The team reached the United Rugby Championship play-offs and made it to the semi-finals of the Challenge Cup.
He says the challenge now is to strengthen further while learning from what didn’t work.
"I'm very confident, obviously, there is a lot of work to do with the youngsters we have in the group. There's quite a long time from now to the first match on the 27th of September, so we are going to put in a lot of hard work, so that we may hit the ground running in round one," emphasised the South African coach.
Reflecting on their quarterfinal loss, Everitt highlighted the team’s attacking efficiency inside the Bulls’ 22 as a clear positive.
However, he admitted their second-half performance ultimately let them down.