Goals from Yoane Wissa, Bryan Mbeumo and Saman Ghoddos sealed a comprehensive victory despite the Bees being without Ben Mee, the suspended Aaron Hickey and Ivan Toney and long-term injury victims Rico Henry and Kevin Schade.
“It was a very good performance and well-deserved win,” boss Frank said.
“Our first half was maybe our best performance this season except we should have been three up.
“I think we should have had more wins than we have had this season and it was a good opportunity to get one against Burnley, although they are a very good team.
“With all the injuries and suspensions, the way we performed and to be that impressive it is definitely up there with one of the best ones.
“But we have to win the next few and stay back on track.”
Brentford are 14th in the Premier League table and face a west London derby against Chelsea next weekend.
