The Welshman's second stint with the Potters came to an end in May after nearly seven years at the helm, with Mark Hughes appointed to succeed him, following a disappointing second half of last season.
After steering the club into the Premier League in 2008, Pulis' side became renowned for their direct but effective style of play.
While Stoke maintained their top flight status, reached the 2011 FA Cup Final and played in Europe the following season, some pundits lambasted Pulis for failing to develop a more attractive approach.
Pulis refused to criticise Stoke chairman Peter Coates for dismissing him after the club finished 13th last term, but passionately defended his work at the club on the show.
"We had six consecutive seasons in the Premier League, we got to an FA Cup final and won the semi 5-0 at Wembley, we got to Europe and have been selling out 27,000 or 28,000 every year," listed Pulis.
"The year we got promoted we had the 13th lowest budget in the Championship and we never spent a lot of money on players.
"Then, if you look at the stats, every year we improved, in respect of possession. I'm not a manager who likes to play back, square and sideways; I was always taught as a midfield player your first touch is to open up and look forward.
"So we played small passes through the pitch, rather than small passes square and the side was strong, organised and fit.
"Stoke have gone from being a bottom half of the Championship club to talking about finishing in the top eight of the Premier League in six and a half years - that's not too bad."
Pulis revealed behind the scenes changes - which he refused to divulge on air - were a factor in his exit from the club, but believes current boss Mark Hughes has been handed a strong foundation from which to take the club forward.
"At Christmas time we played Liverpool and we played really, really well and beat them 3-1 ," he reflected.
"We'd only lost three games at that point but the second half of the season...there's reasons for it, which I don't want to go into now.
"But I had a great ten years [including his 2002-05 spell] at Stoke. I have tremendous respect for the chairman Peter Coates, who is a real football man and has been a great chairman to me and a great friend.
"It wasn't really a surprise when I went because things were going on behind the scenes and there were changes off the pitch.
"But I think I've done a decent job there and they've been magnificent to me.
"Mark Hughes is a good appointment and the players he'll be working with there, compared to the ones he had at QPR, he will notice a marked difference in their attitudes.
"The likes of Asmir Begovic, Ryan Shawcross, Peter Crouch and Matthew Etherington are great lads and lovely to work with."