Peter Whittingham's first senior hat-trick helped the Bluebirds to victory at Bramall Lane and extended United's winless streak to six league games.
But Blackwell, who has seen his squad decimated by injury in recent weeks, felt the Blades were unfortunate not to take something from a thrilling match.
"Things are tough at the moment, but the squad players that came in gave me a great shift and I can't knock them," said Blackwell.
"It was a good performance and on another day it would have been enough to get us a point.
"It's tough when you are losing your experienced players and until we get them back it will be tough.
"But I think we deserved more than we got out of the game, that's for sure and the players showed terrific spirit to keep coming back."
Blackwell was unhappy with the penalty decision that led to Whittingham's first goal, which came moments after Darius Henderson had cancelled out Jay Bothroyd's 41st minute open.
Bothroyd collapsed in the area under a challenge from Henderson and Blackwell moaned: "How a 6'5" lad can fall to the floor like that and the referee is mugged I don't know, but these things are going against us."
Henderson levelled again for the hosts in first-half stoppage-time, but two more goals from the outstanding Whittingham put Cardiff in control and meant James Harper's injury-time strike was no more than a consolation.
"Anyone who saw the game will realise we were unlucky," added Blackwell.
"We've played some good stuff. Because we are a big club and there are high expectations it's always a crisis and I can understand that.
"You have to deal with that and so do the players. Because of the injuries we've had to make crisis signings to make sure that we can get a team out that tries to be competitive. That's the expectation of the club, fans, chairman and myself. But equally you can't put too much pressure on young kids. If we can get the likes of (Nick) Montgomery, (Richard) Cresswell, (Lee) Williamson and (Jamie) Ward back, all of a sudden you've got a good squad but at the moment we are very light."
Cardiff boss Dave Jones was delighted to claim victory but admitted he had been alarmed by some of his side's defending.
"I just felt every time we got our noses in front we went and did something stupid," said Jones.
"I think the players thought the game was won. I think one or two of them thought "that was it, we've done the job" but you can't do that at this level. You just have to keep going.
"In the second half at 2-2 it was difficult for either side to get a foothold in the game," he continued.
"It was ebbing and flowing but once we did get the foothold I thought some of the football we played was scintillating at times. For the fourth goal, you'll go to a lot of grounds this year and not see a better build-up and finish than that."
Jones reserved particular praise for hat trick hero Whittingham, who appeared almost non-plussed by his sensational performance.
"If you go and see Peter in the dressing room you wouldn't think he had scored a hat trick," Jones added.
"He's just sat in there with a cup of tea.
"He has this demeanour about him but the work-rate and quality that he showed was absolutely superb."