Sherwood met with Crystal Palace co-owner Steve Parish last week to discuss taking over at Selhurst Park after Tony Pulis quit as manager just a day before the start of the Premier League season.
But in his regular column with British newspaper The Independent, Sherwood claimed on Friday that he did not feel wanted by Crystal Palace, who kept being linked with other candidates, so he eventually pulled out of the recruitment process.
"The longer the process went on at Palace, and the more names that came up, the more I felt that Steve was keeping his options open," Sherwood wrote.
"It shows the great level of respect for the club among coaches. I know a lot of managers were interested. But at some point, as a manager, you want to know the interviews have stopped and you're the club's first choice.
"That was why, on Thursday night, my agent sent a message to Steve to say that I was no longer interested in being in contention for the job.
"I have to say, I took some persuading in the first place to go to see Steve last Sunday. My feeling at the time was that the race was already run and that the job was going to Malky Mackay. But in the end I thought it would be a worthwhile experience.
"As it turned out the race is still on. It started as a three-horse race, with the runners being me, Malky and, I presume, Glenn Hoddle.
"By yesterday morning it had turned into the Grand National. There seems to be a new name every day."
Sherwood added that he was keen on the job, especially after speaking to other people with closer ties to the club.
"After seeing Steve, I asked people who knew Palace well about the club," the 45-year-old revealed.
"Their immediate response was that they could not put me off the job. The feeling was that Palace was a good club and that the best thing about it was the current group of players, as well as the fans.
"If I had been offered the job early in the process, soon after my interview, I would have taken it."
