Dikgacoi was making his debut for the club but received his marching orders for violent conduct towards the end of the first half with his side already a goal down.
The South African, who joined Fulham from Golden Arrows in the summer, appeared to head-butt Hammers midfielder Scott Parker in an off-the-ball incident which was spotted by the fourth official.
Despite being a goal down, Fulham recovered from the setback to take the lead in the second period, only being denied a win by a late Junior Stanislas strike.
Hodgson was quick to deny any wrongdoing by Dikgacoi and voiced his sympathy with the player as his debut was cut short.
"It didn't look too violent to me, I've got to say," Hodgson told Sky Sports. "The lad has come out of South Africa and was playing his first match.
Disappointed"I don't know what happened between the two players but I'm always disappointed when professional players get sent off for something that the word 'handbags' would be an exaggeration.
"I come from a time of playing football when there was quite a lot of violence on the football field and people actually did get head-butted and get kicked and people got hurt.
"At most you could accuse him of being na?, that I suppose is a crime but he's devastated and he's got my sympathy."
Hodson was reluctant to criticise referee Phil Dowd but reiterated his disagreement with the decision.
He added: "I can't say that I accept it, and I can't say that I think it's a good thing because I think the spectacle would have been better had it continued with 11 against 11."
A Danny Murphy penalty and a Zoltan Gera volley turned the game on its head in the second half after Carlton Cole had given West Ham a first-half lead.
Fulham were resilient for the reminder of the game but were finally undone by Stanislas' deflected strike in injury time but Hodgson remains proud of his players.
He said: "We played so well for all of 50 to 60 minutes playing with 10 men. I thought we did really well to contain them in that period and create chances of our own.
"Of course when you concede a goal in the dying minutes with a deflection it's very difficult to say I'm satisfied, that I'm happy.
"But I'm very proud and very satisfied, more than satisfied, with my players' performances.
Sturdy"I don't think there is any more they could have done, there were some sturdy performances out there and I suppose my disappointment is more for them.
"We'll get over it and we'll take positives from it which was largely the performance."
Hodgson feels his side were always in control of the game even as Cole headed the hosts into the lead after 16 minutes.
"I thought we were very unlucky to be a goal down at that time because I thought we'd controlled the game well and had chances of our own," he said.
"So of course then we went down to 10 men and it was still 1-0, things looked bleak, but the players continued to play in the same way and we kept the ball quite well even with 10.
"And most important of all the defensive organisation was as good as it had been in the first half."