The Robins lost just once in October and are currently on a five-match unbeaten run.
Yates told Sky Sports: "We've got a really good strong group and the staff the players, everyone has gone about the season really well after a disaappointing end to last season.
"Our aim is to build on what we have started with three defeats in 17 and try and get promotion this year."
Yates told the club's official website: "It's a great honour obviously but this award is for everyone at the club.
"My players, my backroom staff and the people who work at the club have made this happen. My name is on the award but it has always been about a team effort at this club and that is what has got this club into the position it is in today."
Yates saw off competition from Martin Allen at Gillingham and Oxford's Chris Wilder to claim the award.
Vale winger Vincent scooped the League Two Player of the Month award.
Vincent had an impressive month in front of goal in October, scoring in Vale's wins over Oxford and Wycombe.
His continued good form and understanding with leading scorer Tom Pope has been a key part of Port Vale's strong start to the season.
The Player of the Month panel consisted of Emma Collins, Wolves legend Don Goodman, BBC Sport's Mark Clemmit and The Football League's Head of Communications John Nagle.
Commenting from npower, Sponsorship Manager Emma Collins said: "There's been a lot of deserved praise for Tom Pope's goalscoring record, but Port Vale are no one-man team and Ashley's contribution this month was clearly worthy of recognition.
"So often the architect of goalscoring chances, we're sure Ashley will have enjoyed his goals this month and will want more as the season progresses."