This loss to London Scottish at Headingley came six days after a record 72-5 drubbing at London Irish and left them rooted to the foot of the table.
It was a frustrating night for Carnegie who showed flashes of enterprise and did some solid work in defence, but let themselves down with basic errors.
Scottish were not exactly in sparkling form themselves, going into the game in ninth place in the table having won only twice in seven games this season.
They looked a cut above in the first half and should have been further than 12-5 ahead at half-time, but Carnegie showed some resilience in defence after a shaky start.
They matched the visitors in the third quarter, but a third Scottish try with 18 minutes left denied Yorkshire what could have been a precious bonus point.
The return of centre Peter Lucock after a four-game injury layoff was a bonus for Carnegie, who included new signing Craig Mitchell following his return to the club from Newcastle.
Carnegie never got on the front foot and suffered an early blow when prop James Thraves was hurt, Will Vaughan taking over off the bench.
Things got worse four minutes later. Tom Bullough did well to halt Scottish’s full-back Joe Luca Smith just short after he had taken advantage of a wicked bounce from a kick by Lucock.
The pressure, however, stayed on and Smith was again involved as Rob Stevenson slid over for the opening try, though Jacob Perry’s conversion attempt bounced away off a post.
Carnegie conceded a flurry of early penalties and one of those led to the visitors’ second touchdown. Matt Williams took advantage of some poor defence in the middle of the field to supply Grayson Hart and his pass sent Miles Mantella between the posts.
Perry’s conversion made it 12-0 after only 13 minutes and there was a real danger Carnegie would be blown away. Though they turned down a kickable penalty soon afterwards, the home team did not threaten until nine minutes from half-time when a try out of the blue got them back into the contest.
Scottish were pressing for a third try when Chris Elder snapped up a loose pass around half way. He turned the ball to Andy Forsyth and Elder sped over from the return pass, but could not add the extras.
This came moments after Smith had looked set to score only to be kept out by a big combined effort from Yorkshire’s right-side defence.
Other than the two early lapses, Carnegie defended well against a Scottish side who were prepared to throw the ball about, though their handling let them down at times.
Yorkshire’s only positive attacking moment, the try apart, came late in the half when George Watkins scattered the defence with a powerful run before Mike Myerscough surged forward from Luckock’s pass, but eventually the defence dealt with Lucock’s low kick as the whistle went.
Yorkshire were put under more pressure at the start of the second half, but Scottish’s lack of ideas in attack was obvious and they failed to take advantage of some poor work by the hosts in the lineout.
Replacement JB Bruzulier was unfortunate to be pulled back for a penalty to Scottish when he looked set to race clear, but there were no opportunities to either team in a flat third quarter.
That was one of a number of decisions that went against the home team and proved a crucial moment in the game as Scottish increased their lead within moments.
The try came off a well-worked scrum move, Mantella finishing smartly at the corner off Smith’s pass after Mike Bright, Rory Brand and Perry had handled.
Perry could not tag on the extra two and Stevenson missed an opportunity to make the game safe when he failed to use his support after one of a host of Carnegie errors inside their own territory.
The missed conversion from Scottish’s third try meant Carnegie were still within touching distance of a bonus point and they finally managed to mount some sustained pressure in the closing stages without being able to apply the final touch.
Yorkshire Carnegie: Brown, Bullough, Watkins, Lucock, Elder, Forsyth, Fox, Thraves, Buckle, Mitchell, Britton, Myerscough, Ward, Bainbridge, Temm. Replacements: Donnellan, Vaughan, Ilnicki, Frost, Currie, Bruzulier, Davey.
London Scottish: Smith, Mantella, Williams, Veratu, Stevenson, Perry, Hart, Brodley, Saunders, Palframan, Hodge, Uanivi, Tyas, Wynne, Bright. Replacements: Harding, Dawe, Waldren, Douglas, Brand, Davidson, Duncan.
Referee: A Woodthorpe.