The Frenchman scored the opener before a Jota brace, coming either side of Joel Lynch's consolation, gave the Bees a 3-1 win over their hated rivals.
The defender, who scored earlier in the season against Eastleigh, was delighted to get off the mark in the league but knows how important doing a first double over Rangers since 1965 was important to the supporters.
“I don't know if it was a great goal, but we took the lead and it was my first (league) goal for this season,” Barbet said.
“I was really pleased but I was more pleased for the fans because of what it means to them - especially QPR, more than Fulham I think.
“We were not really really good, if you compare our last three home games, but we won 3-1 and we deserved to win, so it was a perfect day.”
The goal was Barbet's third in a Brentford shirt after scoring against Charlton in March 2016.