He declined to name who had asked him to leave the race due to his low support so far in the early nominating contests.
"I don't think it's useful to divulge that because they would be certainly unhappy if I did," Carson told MSNBC's Mika Brzezinski Tuesday on "Morning Joe." "But of course. It's politics as usual in Washington, D.C. It's a slimy thing."
The latest CNN/ORC poll
has Carson at 10% support among Republican voters. Donald Trump is leading with 49%, followed by Florida Sen. Marco Rubio at 16%, Texas Sen. Ted Cruz at 15%, and Ohio Gov. John Kasich with 6%.
Carson said he hopes voters recognize that he is everything they say they want in a candidate.
"A lot of times, it's sitting under your nose and they don't recognize it," he said. "There's always a possibility that people will awaken and recognize that just what they were asking for, I have presented for them -- someone who is honest. They can't find any scandals. All the lies that have been told have been debunked."
Carson, who has had one of the larger social media followings among the candidates, said his supporters are keeping him in the race.
"Many of my social media fans are begging me not to get out, continue to support us tremendously and economically," he said. "There's really no reason to disregard what they have to say."
Carson said on Fox News' "Fox and Friends" that voters must remember that he was once the candidate that could beat Trump and Democratic front-runner Hillary Clinton.
"Before the barrage of attacks on me occurred, I was beating Trump head-to-head, Hillary head-to-head and there are those who didn't like that very much. And the people are the only ones who can rectify the situation," he said Tuesday.