“We showed them too much respect in the first half and that can happen for a team that’s just been promoted,” he said.
“I want them to play with freedom, quality and energy and I thought we did that in the second half. I want us to be brave, but not in a naive way. We want to play on the front foot, create chances and win games.”
Nathan Dyer scored the game’s only goal, with visiting keeper Tom Heaton failing to keep out his low shot. Burnley came close to equalising through Lukas Jutkiewicz and David Jones in the second half.
But Swansea withstood the pressure and, following last Saturday’s first league win at Manchester United, are level on points with top-of-the-table Tottenham and Chelsea.
Defeat for Burnley, meanwhile, leaves them still searching for a first Premier League point of the campaign, although their battling display will have been encouraging for Dyche.
SWANSEA: Fabianski, Rangel, Amat, Williams, Taylor, Shelvey, Ki, Dyer (Montero 66), Sigurdsson, Routledge (Tiendalli 90), Bony (Gomis 64).
BURNLEY: Heaton, Trippier, Duff, Shackell, Mee, Arfield, Marney, Jones (Sordell 90), Taylor (Wallace 72), Ings, Jutkiewicz (Barnes 82).
Referee: Craig Pawson (South Yorkshire).