The Lilywhites slipped six points off the play-off pace with five games to go after losing 2-0 to Marcelo Bielsa's automatic promotion hopefuls.
Ben Pearson's 48th minute red card for bringing down Patrick Bamford when clear on goal proved to be the turning point.
It was 0-0 at the time, Bamford going on to score twice when North End were a man down.
Neil said: "It is always difficult to answer questions about your chances straight after a game and a result like this.
"We will have Wednesday off, reconvene on Thursday, go to West Brom on Saturday and give it a right go like we do every game."
Pearson got a straight red for the foul on Bamford and will be suspended for three games in total - one for this sending-off and two more to reflect he had been dismissed twice before this season.
Reflecting on the defeat which was North End's third on the spin since the international break, Neil said: "We went toe-to-toe with Leeds and I couldn't have asked any more of the players in terms of effort and endeavour.
"We could have looked after the ball better at the top end, taken in the first ball to let us build from there, but other than that we played well.
"The game swung on a mistake which led to the red card.
"If there is a team who you don't want to go down to 10 men against, it is Leeds.
"For their first goal, it was a mistake and a bit of fortune on their part.
"Daniel Johnson played a square ball across the pitch which went out of play.
"When it comes back in, Alan Browne goes in for a tackle and it rebounds off their player into Patrick Bamford's path.
"Bamford shifted his feet and to be fair it was a fantastic finish from him.
"At that point do we sit back in our shape and accept we are going to lose or do we go and try and get the next goal?
"We went to find the next goal and got exposed, the second goal killed the game."