Kenny made his first appearance for the south Yorkshire side since last season's play-off final defeat by Burnley after serving a worldwide ban following a failed drugs test.
The 31-year-old was not even able to train with the Blades and only returned to the squad at the back end of March.
After he made several fine stops to keep Swansea out, Blackwell was delighted to have his man back.
"He looked very assured and his handling was crisp and clean," said Blackwell.
"You could say 'what could have been' when you have seen what he's done today. There was a solidity about the back five.
"I felt that if he made an error the fans would accept it, but he looked as if he hadn't been away.
"It was a worldwide ban, he couldn't train anywhere. We helped him hire a personal trainer and a goalkeeping coach and he has been training in a field somewhere.
"He has put a sorry saga behind him and will never have to go through that again."
The Blades won the game thanks to two second-half goals after Swansea had dominated much of the first hour.
Richard Cresswell's 11th of the season opened the scoring in the 62nd minute when he hooked home an impressive volley and the striker played a pivotal role in the second as his pull back was deflected in off Swans goalkeeper Dorus de Vries for an own goal.
And Blackwell was pleased with the effort his side showed.
"It took us a while to settle down but once we got it right we could have gone on further than that," he said.
"I am proud of the players for the desire they showed. If you're a Sheffield United player that is the least that is expected of you."
The defeat sees the Swans slip out of the top six, replaced by Blackpool, and if they are to reach the end-of-season showpiece they must beat Doncaster and hope Ian Holloway's men fail to take three points off Bristol City.
Sheffield United: Kenny, Nosworthy, Bartley, Morgan, Naysmith (Seip 69), Little, Montgomery, Harper, Quinn (Yeates 33), Camara (Evans 64), Cresswell. Unused substitutes: Aksalu, Geary, Fortune, Lowton.
Swansea City: De Vries, Rangel, Williams, Monk, Bessone, Dyer (Cotterill 64), Pratley (Orlandi 75), Britton, Gower, Van der Gun (Trundle 75), Kuqi. Unused substitutes: Cornell, Pintado, Allen, Serran.
Referee: Scott Mathieson (Cheshire).
Blades man of the match: P Kenny.
This season the Yorkshire Post has an exciting new match-day service, called Match Centre. Here you will find minute-by-minute updates, stats and team formations. Plus reports from every game in England, from the Premier League down to the Blue Square Premier.
Simply select your game from the pull down menu, then click on the 'i' information button on the right of the fixture and it will give you access to everything you need to know about your team.
So if you can't make it to a game, head for the Match Centre and we will give you the best seat in the house. Click the link below.
For the latest team news, score and commentary from your team check out our new Match Centre