Butler saw his second spell at Rovers come to an end last week when he reached a mutual agreement with the club to end his deal, which still had a year left to run.
Determined to continue his playing career, the 37-year-old subsequently joined National League North side Boston United.
“It was a really tough situation because Andy just wants to play,” Wellens told the Free Press.
“I’ve been a professional footballer of that age myself and all you want is to play.
“Boston have given him the opportunity to do that.
“I think as a club we’ve looked after him in terms of the pay-up.
“We respect what he’s done for the club. He’s been a fantastic person as a player and when he stepped in as manager.
“We felt it was only right to look after him in terms of the pay-up but it gives him an opportunity to carry on playing.”
Wellens had previously stated that he would need to move players out in order to make more additions to his squad but says he will not have too much money at his disposal from Butler’s departure.
“It will help us but because we’ve looked after him it doesn’t free up that much of what we had,” he said.
“I think it’s more important for us to look after Andy. You’d expect he’d go to Boston and play every single week, which is what he wanted.”