"If one of the world's big clubs comes in for you it's understandable a player might have the desire to go to that next level," said the Trinidad & Tobago international.
"Until you sign a contract with a new club it's all just talk. January was a crazy time and now I have to focus on the games ahead.
"The manager spoke to me. The reassuring speech came out to let me know the club still wanted me. That is always nice to hear.
"But sometimes a big situation like the transfer story can make it hard for the manager to say anything. But as far as I am concerned, we are all needed."
Liverpool are understood to have mooted a loan deal for Jones during the January transfer window, a suggestion that drew an angry response from Sunderland manager Steve Bruce and left the former Southampton player feeling uneasy.
"I didn't have any part to play in that whole situation," Jones said ahead of struggling Sunderland's visit to Premier League title hopefuls Arsenal on Saturday.
"There were stories going back and forth that were disturbing â€' there is no possible way that you can avoid reading anything in the papers but you try and lock yourself away from it as much as possible.
"If you noticed during all of this stuff I never came out and gave any indication that I wanted to leave, that I was unhappy or anything like that.
"For me, that assumption is a bit far-fetched. There was a lot of stuff being said by whoever and you can't stop that.
"All I can do to prove I am committed to Sunderland by showing it in games - and hopefully people can then see it with their own eyes now."
Jones, 25, also paid tribute to the club's supporters who have warmed to the player recently following a series of impressive performances.
"It's nice to hear the fans signing my name in the last two or three games but I think they have been doing it most of the season," Jones said.
"It's great to know that they recognise that when I wear a Sunderland shirt I give it 100 per cent.
"I don't think the fans had any reason to believe that I was behind these rumours, or that I wanted to leave."