United had two players sent off - Andrew Wright and Grant McCann - and conceded two penalties as they were beaten 3-1 by the Baggies.
The straight red card shown to McCann particularly annoyed Adkins, as the Northern Ireland midfielder was sent to the dressing room for dissent.
"I will be going in to see the referee because he has sent one of my players off for using foul and abusive language, but I will be wanting to talk to him about the manner in which he has spoken to some of my players during the game," he said.
"I have to be careful what I say or else money will come out of my pocket. I know the referee does not have access to technology when he is making his decisions.
"But I have looked at both penalties on the DVD, the first was a good challenge and with the second both players made contact with the ball at the same time.
"We also had a player sent off on Boxing Day at Middlesbrough and these decisions are very disappointing."
Roberto Di Matteo defended the second penalty of the game - which was saved by Joe Murphy from Graham Dorrans after David Mirfin's challenge on Luke Moore was deemed a foul - but would not be drawn on Rob Jones' tackle on Dorran that brought the first spot-kick for the visitors.
"As far as the two penalties are concerned, I did not really get a good view of the first decision but the second looked a clear penalty to me," he said.
"I thought we were in control for most of this game. We might have been more than one goal in front by the interval and it was disappointing to see Scunthorpe come back on level terms from a set-piece situation.
"My players had to be careful to keep their discipline because the home crowd were trying to influence the decisions of the referee."