Wales start their Six Nations campaign in Italy on 5 February with Warburton endorsing interim head coach Rob Howley's decision to appoint Jones.
Warburton, 28, has led Wales a record 49 times since being handed the captaincy by Warren Gatland in 2011.
"It's been lovely while I've done it but I can enjoy my rugby without it," said Warburton.
"It allows me to have a little bit more freedom.
"There comes a time in your career you need to focus on yourself. Even though you are in a team sport, you do still need to be selfish."
Speaking for the first time since the decision was announced, Warburton said: "It's something I've known about for a while and spoken about it to Rob.
"There wasn't a definitive moment. This has been happening over the past few months.
"It probably came to our attention during the autumn, when we started talking about it, and through December and January.
"It was a decision we both agreed on and thought was best for myself individually and the team.
"You know it is a big call for a coach to drop his captain."
Warburton insists he is not disappointed and is free to concentrate on securing his position in the Wales back row.
"I found it to be a relatively easy decision because captaincy has never been the motivation for me," said the Cardiff Blues flanker, who said he was unsure whether he would lead Wales again.
"Playing number seven for Wales and the Lions has always been the target.
"It's not something I've been bitterly disappointed about or something I've always desperately wanted to do. It's an honour.
"There also comes a time in your career you need to focus on yourself.
"That's why this is the best thing for me. It will probably make me more hungry not to have the captaincy.
"There are so many good sixes and sevens in the squad, that you have got to bring your A-game just to get in the 23."
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Since 2011, when he took the job aged 22, Warburton has led Wales more times than anybody else and captained his country at two World Cups and to a Six Nations Grand Slam in 2012.
"People expect the Grand Slam to be my highlight, but I only played three games," he said.
"My highlight might be the win against South Africa in 2014 because that was a big moment.
"Players are always getting the question about [beating] southern hemisphere sides. To finally get that win was satisfying.
"When I look back to 2011 when I nearly didn't take it, that would have been the biggest mistake of my rugby career.
"Back then I was completely out of my comfort zone and didn't want to do it.
"But it has helped me develop as a person and a player."
Warburton is replaced by Ospreys skipper Jones who has captained Wales five times and led the Lions to match and series victory in the final Test against Australia in 2013.
"Alun Wyn is a vastly experienced player and has more experience than me at international level," said Warburton.
"He's seen pretty much everything in this game. That's what makes him such a great candidate to be captain.
"Alun Wyn is the stand-out candidate. It will be a nice smooth transition and he will be able to cope fine with things."
Warburton said he was unsure whether his chances of leading the Lions again in New Zealand this summer after captaining the tourists in Australia in 2013 would be affected.
"I haven't spoken to Warren [Gatland] since he was announced as Lions coach," said Warburton.
"He popped in and observed some training sessions, which I imagine he did across the home nations.
"He was informed about the decision by the WRU and Rob spoke to him.
"One of my concerns was Warren, because he has invested a lot of time in me, especially when I was so young.
"But he knew exactly what was going on which was great."
Sam Warburton says he remains as hungry as ever to play for Wales despite losing the captaincy to Alun Wyn Jones.