Vine played a prominent part in St Johnstone's third-placed finish in the Scottish Premier League last season, but was not offered a new deal.
The 30-year-old expected an offer after then manager Steve Lomas hinted they would need to qualify for Europe to meet his wages.
But, with Lomas departing for Millwall and being replaced by Tommy Wright, Vine says he heard nothing.
He was unveiled as a Hibernian player on Monday after signing a one-year deal on Saturday and feels fate has been kind despite a disappointing end to an enjoyable season in Perth.
"I'm not one for demanding things and needing to know where I'm at. I like to think performances speak for themselves," he said.
"I played 37 games and scored seven goals and played wide left and we finished third in the league.
"Everything pointed to them wanting to keep me, I didn't think I needed a conversation.
"I just had a very short conversation with the manager at the time and he said he didn't think the club were going to be able to fit me into the budget, we needed to get third in the league, which we did, and he was going to come back to me after that.
"That was the last thing I heard. He then got the Millwall job which was fair enough, but I didn't hear anything from St Johnstone after that, which for me, I thought wasn't the best way to handle it.
"I've got a lot of friends there and I wish everyone all the best there, but I just thought it could have been handled a little bit more respectfully.
"But if they had been on the phone to me, I might have made a different decision and I'm delighted to sign for Hibs and not particularly concerned about what happened at St Johnstone, because I believe I'm in a better place now."
The former Birmingham and QPR forward had interest from England but was more than happy to continue his stay in Scotland, especially with the Edinburgh club.
Vine, who could make his debut in the Europa League second qualifying round first leg against Malmo in Sweden on Thursday, said: "There were a couple of other things in the SPL.
"When I knew I was coming away from St Johnstone, I told my representatives that I had enjoyed it in Scotland but if I was to come back I would want to play for one of the proper clubs in the SPL.
"And I think Hibs are widely regarded as being up there as a proper football club with proper facilities and somewhere you should enjoy playing your football."
Speaking at Easter Road, Vine added: "I've played in the Championship a lot of my career and League One but having played a season in the SPL, the comparisons some people make are not fair.
"It's a good level and you don't find many places like this outside the Premier League in England.
"There were tentative enquiries from teams in the Championship but when a team like Hibs were interested I jumped on the plane to come up here."