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Manchester-born Dobing is best remembered in the Potteries as Stoke's skipper when they lifted the trophy by beating Chelsea at Wembley in 1972.
Dobing, who began his career at Blackburn Rovers, made 377 appearances and scored 95 goals for the Potters after being signed by manager Tony Waddington from Manchester City for a then club record £37,500 in 1963.
He had already made one previous appearance at Wembley, for Blackburn in 1960, when he scored five times in their run to the FA Cup final, only to lose 3-0 to Wolves.
But his second chance to be a winner at the home of football, still a comparatively rare achievement for any player back then, came approaching the end of his career - and this time he took it.
Dobing scored three goals in the 1971-72 League Cup, the most important of them in the semi-final second replay against West Ham United as the Potters went through 3-2 to reach Wembley and their first major final - and it ended in triumph as goals by Terry Conroy and George Eastham gave them victory.
In a statement, the club said: "The thoughts and sincere condolences are with Peter's friends and family at this immensely difficult time.
"With this coming Saturday being the club's Remembrance fixture, details regarding plans for a tribute to Peter on a forthcoming match day will be shared with supporters in due course."
Dobing's father had played rugby league for Salford, but Peter opted for football, playing as an amateur for both Blackburn and Manchester United before signing a professional contract for Johnny Carey at Rovers in December 1955.
He scored 20 league goals as Rovers gained promotion to Division One in 1957-58, including four in one match against Bristol City.
He then hit a season's best 24 league goals in 1958-59, before Blackburn's run to the cup final in 1960 - and he then moved to Manchester City, also for £37,500, a year later when Denis Law left to join Italian side Torino.
He was City's top scorer with 22 goals but when they were relegated a year later, Dobing moved on to newly promoted Stoke.
In his first season at the club, he scored 19 goals as they reached the League Cup final for the first time, then held over two legs, which they lost to Leicester City.
He broke his leg in January 1965 and was eventually moved back into a midfield role, where he played as Stoke won at Wembley in 1972.
Dobing's second leg fracture proved a career-ending injury and he went on to work as a real life potter in the Potteries.