The defeat means that the club's hopes of reaching the quarter-finals of the Amlin Challenge Cup are now all but over.
But Coombs insists now is not the time for the club to feel sorry for themselves, especially with a RaboDirect PRO12 clash with Connacht fast approaching.
"We have to keep our heads up for when we got to Connacht on Saturday and try and take the positives from the defeat to Bordeaux-Bègles because we are bigger than that," the 29-year-old told the South Wales Argus.
"They were very powerful but in the first half we gave them a platform to play with and gave them too many penalties so they could get their driving lineout working.
"We only have ourselves to blame - you can't afford to give away three yellow cards.
"It was a brave effort by us - as it always is with the Dragons - but we are more than that now."
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