The Lilywhites’ 3-1 defeat to Fulham on Craven Cottage left them nine points shy of the top six with 11 games left.
But Snodin, No.2 to Simon Grayson, isn’t throwing in the towel and the focus is now on Tuesday night’s visit to Derby County.
“These boys won’t give up so of course we still have a chance of making the play-offs,” said Snodin.
“We go to Derby next and we will put up a fight there, then we will have a look at Reading for Saturday.
“As a team and staff we will keep going until it becomes impossible.”
Snodin was impressed by Fulham who bossed long spells of the game and had 71% of possession.
They took a first-half lead through Sone Aluko, with Chris Martin doubling that advantage after an hour.
Preston briefly came back when Tom Barkhuizen scored but Neeskens Kebano made the game safe for the London club.
Said Snodin: “Fulham play their system well and looked very good.
“We played some decent stuff ourselves at times but not for long enough.
“You’ve got to give credit to Fulham, what they do, how they play and the players they have in their side, I thought they were different class.
“Credit to our players, they kept going until the end and at 2-1 we thought we had got back into the game.
“Unfortunately against the run of play, Fulham broke on us and scored the third goal.”
Snodin was pleased to see Barkhuizen on the scoresheet for the first time since he joined PNE from Morecambe.
Rewarded with a first start after five appearances from the bench, the winger found the net after chasing a through ball from Aiden McGeady.
“Tom has been very good in training,” said Snodin.
“He’s been coming along and looking like he can handle this level of football.
“Tom has got that pace which can help any football team and he seems to glide on the pitch.
“For the goal it was a great through ball from Geads and Tom finished it nicely.
“It was a shame we couldn’t get another when on top.”