Neil Warnock's side are in 10th place, five points adrift of sixth-placed Nottingham Forest with nine games remaining.
Despite three successive draws, including the midweek stalemate against Peterborough, White believes they can still snatch a play-off place.
"Obviously Tuesday night was disappointing," White said. "We had a few chances at the end there when we could have nicked it.
"The first half wasn't the best, but we came out second half and gave it a good go.
"Unfortunately it didn't go for us, but in terms of the mood and the belief it's still all there.
"We still think we can get that final sixth spot and keep going for promotion."
Five of Leeds' remaining games are at Elland Road, starting with a derby clash with Huddersfield on Saturday, and White said promotion is still the club's collective aim.
"It's still our target and it's still something we can achieve," he added. "We've just made it a bit harder by drawing a few.
"Other results have gone for us in recent games and if we could have picked up a couple of wins we'd be right up there.
"So from that view point it's a bit disappointing but we'll keep going. I think we can still get there."