Some supporters walked out of a meeting with the board at Dens Park on Saturday after it was confirmed that the 51-year-old former Dark Blues player, whose only previous managerial experience was with Clyde and which ended in 2009, would be taking over following the shock sacking of Barry Smith last week.
Only a smattering of supporters made the trip to Glasgow as Brown sat in the directors' box to watch a Joe Ledley double, a penalty from James Forrest and goals from Dylan McGeouch and Gary Hooper further deflate the relegation-bound visitors who remain 15 points adrift at the foot of the Clydesdale Bank Premier League.
To cap a miserable afternoon Dundee ended up with 10 men after substitute Matt Lockwood, only on for the start of the second-half as a replacement for Brian Easton, was shown a straight red card three minutes after the restart for denying Hooper a clear goalscoring opportunity, with Forrest converting the resultant penalty.
Afterwards Farningham, who will stay on at the club as assistant, addressed the reaction to Brown's return to the club where he was hero as a player.
He said: "It is not John's fault, I have got to emphasise that, it is not his fault. I don't know about John's credentials, all I know is that he will give it 100 per cent and will do everything to try to get the club moving forward and I'm quite sure he will because that is what we have to do now.
"We have big games coming up and the supporters need to get behind the team and the manager. It has been very difficult for everybody, the staff and the players but they have to get on with it."
Celtic took another step towards retaining their title with a convincing if expected win. Hoops boss Neil Lennon said: "We weren't great in the first half but in the second half we were excellent and I am really pleased with the five goals. That's 23 goals in the last five home games so we are really starting to turn it on at home.
"I was pleased with Dylan, it was a great goal and that was our fourth or fifth penalty in a row (we scored) which makes a nice change for us. Gary got his goal which puts him on 24 for the season, so I was delighted with the performance and the clean sheet.
"Ledley was great and deservedly got man of the match, he is a very important player and proved that over the years. He is talking about staying on here and I would like to do that if I could, he is a great player for us."