United led thanks to Andy Butler's strike after 19 minutes, but the game turned after full-back Kelly Youga was shown a straight red card after 71 minutes.
Referee Andy D'Urso decided his clumsy tackly on Stephen Crainey merited an early bath.
That gave the Seasiders the initiative, and just Scunthorpe looked set to hold on substitute Michale Flynn broke their hearts with just a minute-and-a-half of normal time left.
"I thought we should have won, we had the opportunities and we played some nice football," said Adkins.
"The sending off changed the game and we're sitting there with five minutes to go thinking we've got it.
"But that's life and it's no good whinging. We've lost two points. There's no pressure on anyone at this football club for the simple reason that we're on a journey of discovery to be the best we can be.
"Monday and Saturday are games that we thought we could win, but we didn't and we now have to be positive to try and win the next game.
"Goals change games, referees change games and rash challenges change games.
"There were a lot of turning points in this game. The fantastic save from the goalkeeper off Jack Cork, the full-back heading it off the post and the goalkeeper tipping it round the post off Martin Paterson."
Adkins appeared unhappy with Youga's sending off, which came on his first game back after a one-match ban following his red card in the draw at Coventry.
"The sending off changed the game. I thought we were comfortable at 1-0," added Adkins.
"In today's football, you're not allowed to tackle. It's the changing face of football.
"Young Kelly is enthusiastic about what he does and luckily he's not made contact with the lad."
Pools boss Simon Grayson admitted his side had played below-par for much of the game.
"We weren't really at it but at the end of the day we've got another point towards our campaign," he said.
"Scunthorpe are a good team and they work hard like we do, they try to play the ball like we do and we know so much about each other that it was probably bound to be a draw."