Pawlett was criticised by Brown after appearing to go down easily following a tackle by Dark Blues defender Lewis Toshney as he won a second-half penalty at Dens Park.
Niall McGinn rammed home the spot-kick to secure a 1-1 draw for his side.
As a result, Dundee were left seven points adrift at the bottom of Clydesdale Bank Premier League with just six to play for.
Brown subsequently hit out at both Pawlett and referee Alan Muir, claiming the player had "cheated" and that the decision was a "disgrace".
Pittodrie boss McInnes, however, told Press Association Sport: "I was 80 yards away and I thought it was a penalty. I saw the claim from my players at the time, the referees is 10 yards away and the linesman probably closer.
"I think Peter reacted well and showed good pace to a ball that is alive in the box. For me, the big boy Toshney came in and tried to slow down at the last minute but was a bit hasty in his challenge and for me he has caught Peter, there is definite contact and it is a penalty kick and I think it is a right decision."
Brown was joined in his stinging rebuke by Dundee keeper Steve Simonsen, who tweeted after the game: "Having seen the incident again I've changed my mind, we were mugged £diver £cheat don't blame the ref he was conned!"