Saints ran out 3-1 winners at St Mary's on Sunday afternoon, but with the game still goalless, Clarets midfielder Johann Berg Gudmundsson was brought down in the area by Southampton's Virgil van Dijk.
Dean allowed play to continue, and Southampton thereafter earned a convincing victory secured by two goals from Charlie Austin and another from Nathan Redmond.
Austin's second was his fourth in four against his former club, and came from a penalty Dyche felt should not have been awarded.
With Burnley 3-0 down Sam Vokes scored another penalty, the 19th Dean has awarded since the start of the past Premier League season - a higher total than any other referee.
Dyche similarly described that one as "soft", and he said: "The defining point is our penalty - it's impossible it's not a penalty. We struggled two years ago to get decisions. We're struggling so far this season. The first one against Swansea. Arsenal we all know what happened there.
"I must make it clear it doesn't take away from (Southampton) being a good side and being too good for us - but that doesn't half make a difference. If we were 1-0 (up) the whole feeling changes.
"I've seen their penalty. Wow. I don't know where it lives anymore penalties like that in this game. I'm stunned. Our penalty is a soft one, theirs is incredibly soft. It's beyond me how they're given nowadays. Simulation? Possibly."