The Eagles failed to fire in the first period and although they created several half-chances in the second, could not convert to gain any ground on their fellow promotion-chasers.
Holloway said afterwards: "We start slowly, like my car did this morning. But the longer the game went on the better we looked and I find it hard to believe we didn't win, but that's the way it's going at the moment.
"So the players are disappointed, we really want to stay in touch with the top teams and go up automatically, so we have to turn games like that into three points towards the end of the season.
"We were a gnat's wing from taking the three points that I thought we deserved."
The future of star man Wilfried Zaha remains a hot topic of discussion as Premier League clubs step up their interest - but Holloway is focused solely on the present.
He added on the England forward: "Wilf is so exciting, I just want him to get the ball. For him to be talked about is great - but he plays for Crystal Palace."