The Eagles were challenging for automatic promotion two months ago but a run of nine matches without a win left them in danger of relinquishing their place in the top six.
Holloway admitted that run had been a "living, breathing nightmare" but it came to an end with Saturday's 3-2 win over Peterborough, during which top-scorer Glenn Murray ended an eight-game goal drought.
"I think we have got stronger over the last couple of weeks because things had been rosy, then it went wrong and nearly everyone in the ground, bar me, thought we were going to throw it away," said Holloway, whose side face Brighton in the first leg of the play-offs on Friday.
"The players have achieved something by getting in there. It would have been disastrous if we'd fallen out, particularly with Bolton and their old manager Dougie Freedman chasing us. But we are in there.
"To some of our fans that wasn't good enough and they've told me that, but I have to be a realist.
"When I first came here no-one said we had to go up, but we had a chance because of the way we were playing. Now we are in there fighting.
"This is about us having a chance to get the last promotion place to the Premier League. We almost lost it because the players wanted it so badly they got nervous. I don't sense that from them now.
"In life you have to grab things out of the fire and be brave and strong enough."
Palace have a fierce rivalry with Brighton stretching back to the late 1970s, something Holloway was made fully aware of when his side were beaten 3-0 at the Amex Stadium in March.
"What it means to the supporters is immense, they really don't like each other. I understand that now," he added.
"But what I can't do is get caught up in that. I have to focus on their strengths.
"There are four teams in it and no one can tell who is going to win. The best thing about all of this is we are still in with a chance."