The English striker took his chance by scoring all of Burnley's goals in the 4-1 victory, which moved his team into the Carabao Cup fourth-round.
"Jay spoke for himself with his performance and goals," Dyche told the club's website.
"He has come back super-fit and is never far away from the team.
"Barnes and Woody historically have been an effective partnership. There are always decisions to be made, it's not just about scoring a few goals. Everything is considered.
"However, it is very helpful trait for striker to score four goals in a game, no matter who you are playing against.
"But strikers are important to any side and I think we have four very good ones."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!