Tykes' top-scorer Chris O'Grady bagged both goals with a penalty in first-half injury time, followed by a close-range header three minutes after the restart to give Wilson a first victory since he returned to manage the South Yorkshire club six games ago.
Despite the win, Barnsley remain bottom of the Sky Bet Championship table, four points from safety, following victories for fellow strugglers Doncaster and Yeovil.
Wilson said: "I think we fully deserved it. To get three points at this stage is a fantastic return. It just makes people aware that we're not going to lie down and we're still there fighting.
"All the teams at the bottom have shown the same type of attitude, I presume, today.
"So the middle order - the teams in the middle of the table - will be looking over their shoulder and that's all we can ask for, to put pressure on them.
"We had a couple of hairy moments to defend at the end when they were throwing everything at us. Possibly we could have done a bit better with the counter attacking that we had but overall we defended it really well and I thought, throughout the game, we looked in control."
Wilson added: "It is a tough job but it's not just ourselves, that's the thing. We're not cut adrift that we're having to win four or five games to get back into the pack. There's only a couple of wins at most that gets us back in there.
"There's a lot of teams who are very, very capable of beating top and bottom teams and that in itself keeps you on your toes in every game you play."
The Tykes only named six of the seven permitted substitutes for the game but Wilson said that was down to Polish midfielder Tomasz Cywka's name mistakenly being missed off the team sheet.
Blackpool boss Paul Ince did not speak to the media after his side lost for the eighth time in nine league games.
A large section of the travelling support chanted for Ince to leave the club throughout the second half.
The Tangerines, who saw Steve Davies' close-range finish flagged for offside in the 43rd minute, rarely threatened as they failed to score for the fourth successive league game.