Contrary to media reports Carney, 29, made it clear he was not jettisoned by the Major Soccer League club but left after failing to agree terms over a proposed extension to his short-term contract.
And he is now weighing up interest from Europe, the Middle East and also a possible return to the A-League, where the former Sydney FC winger would be under the nose of Australia coach Ange Postecoglou with the FIFA World Cup now less than seven months away.
Carney, who played alongside fellow Socceroo Tim Cahill in New York, remained unbeaten in the nine appearances he made this season for the MLS side after joining the club in August with the side's season ending as it bowed out of the play-offs on away goals.
Insisting he was not cut by the cub, Carney explained: "It was a great experience there playing alongside Timmy and Thierry Henry and a great bunch of players and also fantastic crowds.
"At the end of the season there was an offer there for me but we couldn't agree to terms.
"It wasn't a matter of me not being offered anything - the club were simply restricted under their salary cap and I've chosen not to remain in New York.
"Being there got me playing again after being out of the game for a while (after his departure from Bunyodkor in November 2012) and I only have fond memories of the club and the people there.
"It also helped get me back in the Socceroos again so I am really grateful for that also.
"I definitely haven't given up hope of going to Brazil.
"I am just looking at a few things with my agent and deciding on the next step forward.
'There's some interest from a few of the clubs who we spoke to before I went to the States, so we will see what happens."
Carney was recalled to Australia's squad by sacked boss Holger Osieck for October's 6-0 loss to France and 3-0 win over Canada, and having been a part of Australia's 2010 campaign in South Africa he is hungry to make it back-to-back FIFA World Cups.
Though he was omitted from Postecoglou's first squad for last month's 1-0 win over Costa Rica, his replacement Jason Davidson had an at times uncomfortable night and question marks over the left-back spot may still remain in the mind of Postecoglou, who also has the option of Michael Zullo.