The Brewers had lost their first three games of the 2017-18 campaign, but came from behind to beat Harry Redknapp's charges at the Pirelli Stadium.
Clough told BBC Sport after the game: "I'm delighted. It's good to get off the mark.
"It was important to get to half-time only 1-0 down. It was important to get back to being what we are all about and for 20 minutes we did.
"Sometimes it's not about formations, it's about working a bit harder and we did. We have to play at a tempo and make it difficult for the opposition."
Up next for Burton is an EFL Cup meeting away at Cardiff City on Tuesday night.