"They made it hard for us in the second half but a win's a win and we've got three points on the board. Stephen Ward has a wand of a left foot - it was a great strike, a great goal!" Cork told BBC Sport.
"At 3-0 up we should have made it safer, but we got there in the end. It's always good to have a good start in the Premier League - it means a lot to us and to all the fans that came here and those at home."
Cork, who started his professional career at Chelsea, joined Burnley on a permanent deal from Swansea City earlier this summer.