Vine played a prominent part in St Johnstone's third-place 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.
He has been unveiled as a Hibernian player after signing a one-year deal on Saturday and feels fate has been kind despite a disappointing end to an enjoyable season in Perth.
The forward told Press Association Sport: "I'm not one for demanding things and needing to know where I'm at. I like to think performances speak for themselves.
"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."
- Sports & Recreation
- Steve Lomas
- Scottish Premier League
- St Johnstone