The 34-year-old has been part of the Easter Road first team for 17 seasons, but admitted he ‘hated’ aspects of the most recent season.
"At times I have enjoyed it, there have been times I have hated it, and I have been as frustrated as the fans have been.
“We’ve obviously not had the season we were looking for in the league. We have had some good moments, some very nearly moments and it could have been a lot different.
“I genuinely think the club is going in the right direction – we just need to stick together and make sure we give the Hibs fans the season they deserve next season.”
Stevenson has a year left on his existing contract but has no plans to slow down ahead of his 18th season as a senior Hibee.
“I am getting on a bit now but look, I have another year on my contract, so I will give it everything next year and see where that takes me.”
Stevenson also revealed he had been overcome with emotion after winning the Players’ Player of the Year award.
“To get voted for this award by your team-mates and your peers who you work with day in day out, makes the award really special as it shows your work is appreciated.
“I genuinely got emotional watching the videos and hearing the nice words. It was lovely, so thanks very much to them,” he added.