Jim Goodwin claimed coins and other projectiles were pelted at him by Aberdeen “bad eggs” at Tannadice.
The Irishman, sacked by the Dons on January 28, was named the new Dundee United manager on Thursday.
His first game in charge of the Tangerines was against his former club, who won the cinch Premiership contest 3-1.
The Dons took the lead through Duk and although Jamie McGrath equalised from the spot, further goals from Ross McCrorie and Marley Watkins sealed the points for the visitors.
Goodwin said: “I obviously wasn’t expecting a warm reception from the Aberdeen fans.
“But I was disappointed that there were coins and other projectiles getting chucked down on top of me.
“There was a pie, a cup of juice, a couple of coins and unfortunately one of them landed on the top of my head.
“Thankfully it was nothing serious but not what you want when you go to your work.
“I have to say that it is definitely just a minority. There are always a few bad eggs who tarnish the rest of the club.
“Aberdeen is a terrific club and one of the best supported in the country – 2,500-3,000 of them down the road tonight supporting their team but a few mindless idiots have us talking about stuff we don’t want to be talking about.
“It was disappointing but I am not going to go over the top with it and I am sure it will be dealt with.”
Goodwin also commented on a smoke bomb thrown by Dons supporters that came close to hitting one of their own players.
The 41-year-old added: “I understand why supporters like the flares but one of the flares that was chucked on nearly hit Ryan Duncan in the head.
“I think we have CCTV at all of the big clubs now so we need to identify these individuals and make sure it gets dealt with before something serious happens.”
Goodwin also insisted his new charges deserved to take something from the game, adding: “I can imagine how the Dundee United supporters will be feeling going home from that game tonight. I don’t think we deserved to lose the game.”
Interim Aberdeen boss Barry Robson praised his players after they secured their first Premiership away win since October.
Robson said: “It is no secret that the away form has been the Achilles heel for a while now.
“The biggest thing for me – and I have been saying it to the players all week – (is) let’s change it and change it now.
“To be fair they did, they fought for the club and each other.”