Vine spoke of his disappointment at the way his Saints career ended as he was unveiled as a Hibernian player on Monday.
The forward claimed former manager Steve Lomas had hinted the club could keep him if Saints finished third in the Scottish Premier League but heard nothing after a top-three place was wrapped up.
But Wright thought Vine was fully aware of the club's position.
The Saints manager said: "I like Rowan, and Steve and myself wanted to keep Rowan. We were disappointed to see him go but financially we couldn't keep him.
"I think he's quoted as saying Steve promised him something. I don't see how Steve could have done that because we were told we couldn't keep Rowan.
"I don't know what happened in any conversations he had with Steve but I know the chairman had informed Steve and myself that we couldn't keep him.
"He did get a letter from us and his agent was made well aware that we weren't keeping him, so I don't know what happened between him and Steve.
"I like Rowan, I had a great text message off him when I got the job, and I wish him all the best at Hibs.
"And as he said, he has got an opportunity to play at a bigger and better club and we have got to accept that - that sometimes we can't hold on to players that do well for us because financially we can't compete with other clubs."
Along with Vine, St Johnstone have lost key players Gregory Tade, Liam Craig and Murray Davidson this summer.
But Wright is happy with the way his squad is looking ahead of the Europa League qualifier against Rosenborg in Norway on Thursday after bringing in the likes of Rory Fallon, David Wotherspoon, Gary McDonald and Brian Easton.
"Like most Scottish clubs, we have lost a few players but I'm happy with the business we have done," Wright said.
"I wanted to bring in good quality players and cut the budget at the same time, and we have managed to do that.
"I am more than happy with the squad we have got. I do think we need one more in and I'll work closely with the chairman over the next couple of weeks to do that."