They took an early lead through Andy Crosby's penalty, but had conceded three by the time Martin Paterson pulled one back for the Iron
"It was a cracking game wasn't it? It was a good team performance and we competed well against an excellent side," said Adkins.
"We were very unfortunate to lose our captain to a thigh injury and they got a lift from their equaliser.
"The crowd went a little bit quiet and for that 10 to 15-minute period they were in the ascendancy.
"It's ended up 3-2 but we could have got a point in the end and have entertained our supporters.
"We're on a journey of discovery and we've pitted our wits against the best of the best.
"It's the first time we've been beaten here in the league since December 16, but it was a cracking game."
West Brom boss Tony Mowbray praised United, but was critical of referee Graham Salisbury for the first-half penalty awarded against his side.
"I think that justice was done in the second-half and I think that we deserved to take the points,".
"Credit to Scunthorpe and we had to be respectful of their record and what they achieved already this season."