But this victory, his first since returning to the club as manager last month, will go a long way towards placating those who claim drastic action is required to ensure the club mount a serious challenge for promotion next term.
A dismal campaign has forced those hopes to be shelved for this year.
But Blackwell hopes a win, earned as much through the brilliance of goalkeeper Paddy Kenny as James Beattie's second-half strike, marks the start of the healing process.
"It's always nice to come out on top," Blackwell said. "But the precursor to doing that is a performance and we produced one out there.
"It will have gone a long way towards helping the confidence. It's been a while since we took all three points and, although we haven't lost many, perhaps we'd forgotten a little bit how to go and win one.
"But we've done that now.
"We needed that result and although we had some good luck at times we worked our socks off and so I reckon we deserved it."
No-one more so that Kenny who produced a series of fine saves, most notably to deny Russell Anderson and Jamie Mackie as Plymouth pressed for an equaliser following Beattie's intervention.
But the remaining parts of the visitors' defence were resolute too, with Gary Naysmith, Chris Morgan and Matthew Kilgallon all hacking efforts off the line.
"That's the capability of Paddy Kenny," Blackwell, who knows a thing or too about keeping clean sheets himself, continued.
"If you are in the back four and you see him behind you then it gives you a lot of belief.
"But the art of defending is not just about heading and kicking.
"It's also about knowing who to mark, when to pick someone up and when to let someone go.
"We've got a talented squad but hard work will always beat talent if talent does not work hard."
Having drawn six of their previous eight outings and without a Championship success to savour since January, United were under no illusions about the size of the task awaiting them at Home Park.
Paul Sturrock, celebrating his 200th game in charge of Argyle, might not have the same wealth of options at his disposal as Blackwell.
But the former Sheffield Wednesday chief has masterminded a remarkable transformation in fortunes on the Devon coast and his men started the afternoon in possession of the fourth and final play-off spot.
Sturrock implored the rest of the division to take Argyle's top-six credentials seriously before kick-off.
Although this defeat, only their second in seven games, represents a serious blow to their hopes of delivering Premier League football to the city for the first time in its history, it should be far from fatal.
"Perhaps this is going to be a wake-up call for us," he admitted afterwards.
United have ignored far too many of those since being controversially relegated last year, but finally the message appears to be seeping through.
Having inherited a squad high on quality but low on self-belief, Blackwell cutely resisted the temptation to perform major surgery and opted to impose a no-nonsense regime based on industry and endeavour instead.
Plymouth looked the more cohesive unit during a dour first-half ruined in by the elements and a disaster of a pitch.
Jermaine Easter and the dangerous Peter Halmosi both went close but, another Easter opportunity apart, United were the stronger of the two during the opening exchanges of the second and they should take great encouragement from the fact that their goal came from the type of move they have worked long and hard on at the training ground since the new regime was installed.
Its beauty was in its simplicity with Beattie starting and finishing the decisive passage of play.
United's record signing swept the ball into David Cotterill's path before continuing his run and dispatching the on-loan winger's centre.
Kenny, who had already foiled Easter at the near post after former United midfielder Lilian Nalis split the Blades' rearguard with an incisive pass, was called into action again to prevent Anderson's defelected effort nestling in the back of the net.
Kenny was called into action again at the death to foil Mackie.
"I do feel aggrieved not to have taken something," Sturrock admitted.
"We weren't clinical enough but you've got to give credit to United because they were well organised and their centre-halves, I thought, did a sterling job. Football has a habit of kicking you in the teeth when you're on a high."
United know all about that but, on this occasion at least, they got what their efforts deserved.
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The full article contains 876 words and appears in Sheffield Star newspaper.