Jokanovic’s men created a number of good chances but were unable to find the net and were punished when Keshi Anderson struck the only goal of the game in the 76th minute.
Iliman Ndiaye had an 11th-minute header for the hosts ruled-out for offside, while they also had opportunities through Lys Mousset and Morgan Gibbs-White.
“We’re disappointed. We played good football and created a lot of chances and, after one big mistake, we conceded a goal,” said United boss Slavisa Jokanovic.
“Our reaction after the goal was poor. We didn’t have enough power to change our story and it was unacceptable.
“I don’t remember them creating something before the goal. We didn’t play bad. I can’t give an explanation how we lost the game. Today was a really good chance for us and I felt we played better than Blackpool.
“It’s not easy because people inside the stadium aren’t satisfied, of course.
“It is not enough for the Sheffield United supporters, I accept, but the process must not stop.
“I expect we will show more reaction and play a complete game, not some part of the game like today.
“We are in some kind of process, but the process is now a few months.”
Jokanovic made one change to his starting line-up, with Gibbs-White returning after suspension in place of Oli McBurnie.
An early effort from Oliver Norwood saw the United midfielder’s long-range shot clear the bar.
Ndiaye found the net with his header, but the home side’s celebrations were cut short by an offside flag.
Blackpool threatened when James Husband got to the left-hand byline and played the ball across the face of goal, with Jerry Yates just failing to get a touch.
Josh Bowler then played a free-kick into the area which evaded everyone, and goalkeeper Robin Olsen did well to dive at full stretch and turn the ball wide of his right-hand post.
The home side then had a couple of good chances, with Mousset firing straight at Daniel Grimshaw before Ndiaye shot wide from inside the area after a great through ball from Gibbs-White picked out his run.
Gibbs-White had a low shot saved by Grimshaw in the opening minute of the second half, and the Blackpool keeper then produced a superb save to keep out another effort from the same player.
As the hosts continued to apply pressure, Mousset saw his shot strike the underside of the bar before being cleared.
A double substitution for the visitors saw Bowler and Yates replaced by Demetri Mitchell and Sonny Carey.
A change for the home side followed, with David McGoldrick taking over from Ben Osborn.
George Baldock fired over from just inside the area as the home side looked to capitalise on their dominance, before Blackpool threatened on the break, with Anderson’s deflected shot turned wide by Olsen.
McGoldrick then had a goal-bound shot blocked, but the hosts then lost Mousset to injury.
After Carey’s drive was deflected over, Blackpool scored in the 76th minute when Anderson received the ball and cut inside and curled the ball into the roof of the net.
Jokanovic sent on striker McBurnie in place of midfielder John Fleck to bolster the attack, but United never threatened to equalise.
Critchley hailed an effective away performance from his side after they weathered plenty of pressure from the hosts.
“I suppose 1-0, when you keep a clean sheet and you score a goal like we’ve scored, you have to say it was (a perfect away performance),” he said.
“We knew we were facing a very good team today and a lot of the Sheffield United supporters will go home unhappy, but I’ve got no doubt this Sheffield team, if they keep playing the way they are, will be up there at the end of the season.
“In preparation for this game, I was speaking to the staff and the analyst and I honestly thought this was our toughest game this season.
“I think the way that they play, the positions that they take up on the pitch and how they control the game, gives you real problems.
“We’ve rode our luck a little bit at times and the keeper’s made a magnificent save.
“They hit the crossbar and they missed a big chance in the first half.
“It’s that fine line in this division and we’ve scored a magnificent goal to go on and win the game.”
Sheffield United: Olsen, Baldock, Egan, Davies, Stevens, Gibbs-White, Norwood, Fleck (McBurnie 81), Osborn (McGoldrick 63), Ndiaye, Mousset (Sharp 74). Unused substitutes: Basham, Foderingham, Hourihane, Norrington-Davies.
Blackpool: Grimshaw, Lawrence-Gabriel, Ekpiteta, Keogh, Husband, Bowler (Mitchell 63), Wintle, Dougall, Anderson (Garbutt 87), Yates (Carey 63), Madine. Unused substitutes: Connolly, Dale, Moore, Sterling.
Referee: Tony Harrington (Cleveland).