"We deserved to win," Gillot told reporters. "We could even have done our goal difference a bit more of a favour, because we had some chances at the end of the match.
"The penalty got Nice back on track somewhat, but on the whole we ran the show. We did what we needed to in terms of our challenges and our pass game.
"We were concerned with drawing too many games, but now with three wins in our last four matches, we're getting back towards the upper reaches of the league table."
Bordeaux host Nantes in their next Ligue 1 match on Sunday.