Bottom side Dees need Hibs to avoid defeat against fellow relegation rivals St Mirren on Saturday if they are to have any chance of extending their fight against relegation for another week.
After watching the William Hill Scottish Cup finalists draw a blank at home against the Dons, Brown said that he "didn't see any hunger, desire or willingness to put their foot in," while predicting a result for the Buddies in Leith.
Fenlon, though, alluded to the former Rangers defender's on-going links with his former side - Brown stood on the steps of Ibrox last summer and raised questions about the Charles Green-led consortium's takeover of the club - as he responded to his disparaging comments.
"Obviously we know what he is trying to do but I'm not really too concerned about it," said the Dubliner.
"There was only one team on the pitch (on Monday) when you looked at the game.
"We created three or four really good chances so I am not worried about what he has to say.
"I have a big job trying to manage Hibs, he seems to be able to manage Dundee, Hibs and Rangers at the same time.
"I don't know how he does that - I am busy enough doing this one. I don't need any pressure from outside, I put pressure on myself to win football matches.
"You will probably be better off asking him what is his thinking behind it."