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."
The result left 14th-placed Burnley a point above the bottom three and took Southampton up to eighth ahead of their Europa League trip to Inter Milan on Thursday.
Their total of 34 shots was the highest of any Premier League team in one match so far this season, but even after two further goals from Austin gave him a record of seven in his past six games, manager Claude Puel refused to guarantee he would start at Inter.
Asked if Austin's impressive form made him undroppable, the Frenchman said: "No, it's important he doesn't play all the games from the start
It's important you don't lose Charlie, it's important he's available every time, to keep a good physical level for every player.
"Charlie is not an endurance player; it's important to keep him with his qualities, and we can change the team every game
It's not possible, for me, for a player to start all the games every three days.
"We can keep all the players with a good performance all the time, and a good physical level
It's important to conserve (their energy), to continue this work for the team, for the future."
Puel was also asked about the England prospects of Austin and the similarly-impressive Nathan Redmond, and he said: "I would like a selection for all of my players
Many have good qualities.
"Two players, for example, had a good game
I'm happy for (Austin), for us
He likes to score
The team plays good football and takes confidence from Charlie's quality
At the moment he's very important and interesting for us."
Source : PA
Source: PA