Juan Imhoff scored the only try for the French club in a Heineken Cup victory Burnell claimed was well-deserved.
"We won't be getting carried away with this win," Burnell said.
"We deserved the win and we really fronted up against a formidable Racing Métro side.
"We more than matched them physically and proved we are a good side and I cannot fault the commitment and attitude of any of our players.
"Not many sides will come to France and achieve what we have done here."
Racing dominated the opening stages of play with Gaetan Germain scoring the first of 12 points of the evening with a penalty and Argentine-star Juan Martin Hernandez landing a drop-goal.
Cardiff hit back with a try through Filise as the ball popped out of a maul just after the ten-minute mark, which Parks converted. However, the Welsh side were dealt a huge blow soon after with Jamie Roberts leaving the field through injury.
Germain and Parks exchanged penalties before Racing winger Imhoff brushed off three Cardiff defenders to score in the corner. Cuthbert scored a try of his own three minutes before half-time.
Parks continued to add to his score tally in the second-half, despite a drop-goal attempt hitting the crossbar.
The Blues defended intelligently against the Racing ferocious attack and Scottish fly-half, Parks, kicked his side to victory.
"We will enjoy this win but it now makes our next game against London Irish, who we all know are a very good side indeed, more important.
"We have to get something out of that game but this win away in France should give us some real confidence for the rest of our European campaign."
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