Wales named an initial 32-man squad for north America tour which was reduced to 26 when four Dragons players - Charteris, Jason Tovey, Lewis Evans and Dan Lydiate - were ruled out because of the Heineken play-off.
Glasgow outside-half Dan Parks kicked four penalties as the visitors defeated the Dragons four penalties to two.
Opener Croft's 23 came from just 13 deliveries, with four boundaries as the Dragons set a pace close to seven runs per over.
Carey, who took charge at the Racecourse when Denis Smith was sacked in January, saved Wrexham from relegation after the Dragons secured four victories from the final five matches of last season.
BBC: SPORT | Football | My Club | Wrexham | Carey job under threat - Dickens
Ceri Sweeney sparked a frantic finale as his late try and conversion brought the Dragons to within four points.
The playoff system has produced three Welsh winners from four matches with Newport Gwent Dragons going through on two occasions and Cardiff Blues once.
Toulouse took less than four minutes to cut the Dragons' defence open as Skrela's floated pass found Medard, who nonchalantly kicked ahead and gathered a kind bounce.
However, despite leading with 20 minutes, the Dragons were outscored by four tries to three in what the head coach saw as a "disappointing" loss.
Warrington eventually gained some consolation when loose forward Grix supported a break by Michael Monaghan to score but the Dragons cut loose with four further tries in the final quarter.
The double blow for the Dragons is that the four of their players who have been selected for Wales' summer tour to North America will now have to withdraw from the national squad.
The Dragons sit last of the four Welsh sides in the Magners League and face the prospect of a play-off in Italy.
The visitors made a nervous start against the wind and rain at Rodney Parade, where the Dragons had won their last four matches.
They are currently four points behind 11th-placed Catalans Dragons.
But the Dragons, unbeaten in their last four games, hit back immediately, courtesy of indiscipline from Thorman.
Holders Wigan, who beat amateur side Haltom Simms Cross in round four, have been handed a trip to Doncaster Dragons.
The Welsh Rugby Union and the Wales' four regions - the Blues, Ospreys, Scarlets and the Dragons - are discussing a a new Participation Agreement to govern the game in Wales.
The Shield, which has been won by Saints for the past four years, will actually be decided next Friday when Saints face Catalans Dragons at home while Leeds are at Salford.
That four-point gap could have been brought back to one when the Dragons were caught offside five metres from their own line, but the Ospreys opted for a scrum instead and wasted their chance.
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