The Turf Moor club also beat Nottingham Forest to advance to the next round of the Capital One Cup.
The Clarets are unbeaten in their last six league matches and are currently top of the Championship table being the second highest scorers in the division.
Dyche told Sky Sports News: "The players deserve all the credit. Talk of promotion is miles away. We've had a good start to the season. We've performed well. The challenge is to do that on a weekly basis, see how many wins you get and take it from there.
"We're happy with the situation, the team are performing, (and) if you're doing well teams want to knock you off your perch. It's a tough division, we know that."
Elsewhere, Preston manager Simon Grayson has collected the award for League One.
Grayson's Lilywhites won all four of their league games during September and are up to fourth in the table.
The former Leeds and Huddersfield manager started with one win in six and said: "We were very calm at the start of the season, we never lost those games we drew them.
"We had a slight change in formation, went to three at the back and played and grew into the system and I'm delighted we've won five on the trot and got to where we are (fourth) in the division."
And the manager of another north-west club, Rochdale's Keith Hill, is the award winner for League Two.
The Spotland outfit enjoyed four victories - all by a single-goal margin - during the month to move from 17th to fifth in the table.
Hill said: "We went to Oxford at the end of last month and picked up a creditable 1-1 each so we knew we could compete with the best in the league. We looked at the month of September and we knew there was an opportunity to pick up points and really invade the top six, and that's what we've done."
Meanwhile, David McGoldrick, David Mooney and Antoni Sarcevic are the Sky Bet Players of the Month for September.
Ipswich Town striker McGoldrick netted four Championship goals during the month, two apiece against Middlesbrough and Brighton.
Mooney of Leyton Orient was the choice for League One having scored four goals in as many games.
And Fleetwood Town midfielder Sarcevic collected the prize for League Two.
The summer signing has been a key figure in the club's rise up to fourth in the table.