The England international, 23, claims he was unfairly targeted by their supporters prior to his departure from the Liberty Stadium and labelled his exit "Swansea's loss".
"The Swansea fans got on my back a bit at the end, without knowing what was going on behind the scenes," Shelvey said.
"I was training hard and competing for a place in the team. I'd played the majority of games in the season and picked up five bookings - I was suspended and didn't come back.
"I never got a chance of getting back in the team so I felt I was a bit hard done by. The fans got on my back and said I had a bad attitude without really knowing what was going on behind the scenes.
"Obviously it is going to be Swansea's loss in the end. I'm just lucky enough to find a club in Newcastle that have shown interest in me."
But Curtis, while acknowledging Shelvey's clash with supporters, insists the deal was simply the right move for all involved.
"I don't see how he can direct any criticism towards the club," the manager said. "He certainly wasn't hounded out of the club in any way.
"Obviously, there was a little bit of trouble between Jonjo and a small section of supporters but even during the [FA Cup] game last Sunday at Oxford [United] a lot of the crowd were cheering his name.
"It was just a case of Jonjo wanting to play first-team football and in the end it was probably a good deal for both parties.
"The money was good and it was probably good for Jonjo to move, it was in the interest of both parties for him to have a fresh start.
"We have had a disappointing season and I think, hand on heart, Jonjo would say that he has probably had a disappointing season as well.
"I have stated in the past, quite recently, that I wanted him to stay. He wasn't in the team, but he was always going to get an opportunity to get back and from there it would have been up to him."