The England international, 23, left Swansea to join Newcastle for £12m.
"I won't go into it but I felt a little bit hard done by to be fair down there," Shelvey said.
However, Swansea interim manager Alan Curtis responded: "I don't see any criticism that he can direct towards the club."
Shelvey added that things had been fine for most of his two-and-half season stay at the Liberty Stadium.
"I loved the Swansea fans, they were brilliant with me, right through all the time I was there," he said.
"It was just towards the end that there were things being written about me, a lot of rumours, when no one actually knew the full extent of what was going on behind the scenes."
Shelvey's performances this season frustrated many Swansea fans and he clashed with a section of supporters at the end of his final game for the club, the 3-2 FA Cup defeat at Oxford United.
He had started just three Premier League games since October before moving to Newcastle on a five-and-a-half-year deal.
"I didn't ask to leave Swansea or anything, I've never come out and said that I wanted to leave Swansea," Shelvey added.
"I think the manager said to me I wasn't going to play much and I didn't suit Swansea's style of play.
"I thought I was hung out to dry for a little bit when I was training well, I was competing well in the week and was finding myself really unlucky not to play.
Shelvey signed a four-year contract extension with Swansea in 2015 but was the first player to leave since Alan Curtis took charge.
The former Charlton player arrived at the Liberty Stadium in July 2013 from Liverpool and helped the Swans to their highest Premier League finish of eighth in the 2014-15 season.
Curtis said Shelvey was not "hounded out" of club and should not direct any criticism at Swansea.
"We've had a disappointing season, and I think Jonjo hand-on-heart will say he's has a disappointing season as well," said Curtis.
"I think it's been a good deal probably for both parties - he gets a fresh start and hopefully we can use the money to attract other players into the club."
Newcastle United midfielder Jonjo Shelvey has hit out at fans of former club Swansea City, who he feels "jumped on his back."