Warnock returned to Selhurst Park for a second spell as manager on Wednesday, four years after leaving the club to join QPR after Palace went into administration.
The vastly experienced 65-year-old said that he could have returned to the Premier League outfit if Pulis had not performed a U-turn and accepted the job last November.
"Before Tony came there was a possibility that he wasn't going to and we talked then. But then he changed his mind and they did fantastically." Warnock said.
"[Co-chairman] Steve Parish has always known that I am available."
Warnock's surprise appointment comes after Malky Mackay looked set to be appointed before allegations over inappropriate text messages sent during his time at Cardiff City ruled him out of the running to succeed Pulis.
Tim Sherwood then opted to rule himself out of contention and Parish last week admitted that finding a new manager was proving to be a struggle before he finally opted to turn to Warnock.
And Warnock insists he has no problem with the fact that he was not first choice, which was the reason for Sherwood ruling himself out.
"I wasn't really looking to get back into management, but it's not often you get a chance to repay a club that's really helped you, so it's great to have that chance," he said.
"[Parish] just had to go through the candidates like he did.
"He said he never offered it to anybody beforehand and if I'm honest I'm not really bothered or what the betting was.
"I'm just glad that I'm here now and I'm not bothered how many were in front of me."
