Biggar has been restricted to just three appearances in the GUINNESS PRO12 so far this season after being on World Cup duty with Wales, but scored all 19 of the Ospreys' points on Saturday - nailing four penalties and converting his own try.
And the 26-year-old - who finished last season as second-highest points scorer in the GUINNESS PRO12 - was impressed his side got the job done despite being below their best.
"We're obviously delighted to pick up four points, we would have taken that at the start of the day," he said.
"But we've given away soft penalties and soft field position and fair play to Bordeaux, they picked a team to come and play and put us under pressure.
"So we're pleased to come away with the win, but there is a lot to work on ahead of the game next week.
"We were a little bit impatient and forced some offloads which weren't on. They held on and picked up a great try, we're massively disappointed we let them into the game.
"But let's give ourselves a big pat on the back as well because we're in a good position to qualify from this pool now and we have to back it up next week.
"We were far from perfect today but we managed to get a good win after not playing at our best."
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