They had savoured just one Championship win all season before Christmas so defeating a Cornish Pirates side that sat third should resemble a huge success.
However, Stirling demands more; he knows it should have been a far more emphatic result than the final scoreline suggests.
The usually reliable Jacob Umaga missed two penalty attempts and somehow Carnegie ended up clinging on at the end with 13 men following a couple of late, avoidable yellow cards.
At a full complement, the hosts were 18-10 ahead and in control, their set-piece so dominant that after the Pirates’ scrum wilted for a fourth time in quick succession, tighthead Tyler Gendall was sin-binned in the 71st minute.
Carnegie drove the line-out close and forced yet another penalty but somehow it was reversed following a melee and, instead, Josh Bainbridge was yellow-carded.
Then, sensing a reprieve, the visitors broke downfield and looked destined to score before Andy Forsyth’s deliberate knock on.
The Carnegie centre was sin-binned; there could even have been an argument for a penalty try.
Javier Rojas Alvarez converted the penalty and, when Carnegie’s restart rolled dead, Cornish had one last chance.
To their credit, though, the hosts’ defended the final moments brilliantly, something which may not have happened four months ago.
It was a sixth successive win in all competitions and, more importantly, a second consecutive league victory following the triumph at Doncaster Knights that lifted them off bottom.
Although they remain 11th, they are now level with Richmond in 10th who they visit next on Saturday.
Stirling said: “We’re probably five per cent off really putting a good performance in there.
“If we can eliminate some of the poor decisions and individual errors and sort the discipline out too, we’ll be getting there.
“That turnover penalty at the end was a drive-over try for us and conversion so, instead of 18-13, it’s 25-10 and we’re forcing them to try do something.
“But we gave it away and they’re then scoring at the other end.
“This was a litmus test for us and we passed the test. But not with flying colours.
“That said, Pirates were third and playing consistently well and we’ve won six games on the bounce so we have to be pleased.
“We’ve got a good idea now of knowing what we can achieve.”
With former England boss Stuart Lancaster watching on from the South Stand terrace, Carnegie started the more positive of the two sides yesterday.
They quickly got the first try when prop Marc Thomas got over via a smart line-out drive in the eighth minute. Cornish fly-half Will Cargill had been penalised for not releasing to concede the penalty that led to the kick to the corner.
In the process, he also went off with a bleeding mouth and was unable to return, perhaps contributing to his side’s early issues.
Carnegie did ask plenty of questions, one quality midfield move threatening winger Chris Elder to get clear, while their kicking in a difficult wind caused chaos for Pirates full-back Kyle Moyle who twice spilled.
The conditions also saw Cornish suffer in the line-out initially, their first being blown back to the Carnegie side, but the home side also applied plenty of pressure of their own in defence.
Centre Pete Lucock put one huge hit on Rory Parata, the luckless Cornish centre who was also rattled by Elijah Niko, the giant New Zealander winger who forced one of a raft of first-half turnovers with his thumping tackle. Niko, making his first Championship appearance since arriving from French club Beziers, scored his third try in as many games in the 28th minute.
However, it was Dan Temm who proved the architect, the in-form No8 making the break from deep before timing his pass to perfection.
Umaga failed with his second conversion attempt and, in fairness, the visitors hit back strongly having fallen 12-0 behind.
They began to control the ball better and worked their way into the game although their response was slightly fortunate.
Carnegie had actually defended a line-out close to their own line and turned the ball over - only to spill with their first drive out. Cornish hooker Sam Matavesi picked up and had a simple 10m surge to the line as the hosts failed to quickly realign.
Alvarez, Cargill’s replacement who had also missed one earlier penalty attempt, improved and added a penalty on the stroke of half-time to leave them trailing just 12-10. Still, Umaga slotted his first penalty early in the second period and put them further ahead as the scrum got on top.
With ex-Brumbies prop Nic Mayhew coming on for his debut, there was no let-up for Cornish who could not deal with the pressure – until late on.
Yorkshire Carnegie: Umaga; Elder, Forsyth, Lucock, Niko; Te Rure, Bruzulier; Thomas (N Mayhew 62), Buckle (Donnellan 78), Mitchell (Foster 54), Romaine (Lemalu 40), Smith, R Mayhew, Bainbridge, Temm. Unused replacements: Wilson, Wolstenholme, Watkins.
Cornish Pirates: Moyle; O’Meara, Parata, Patterson, Cant (Evans 70); Cargill, Day (Ashby 70); Walker (Andrew 61), Matavesi, Gendall, Freeman, Beukeboom, Caulfield (Lee 54), Stevens (Walker 74), Duncan (Bolwell 54). Unused replacement: Gibbings.
Referee: Matthew O’Grady (RFU).