McGregor was sent off for the challenge on Mohamed Diame which resulted in his injury, with referee Mike Dean also awarded a penalty which led to the Hammers taking the lead.
And Tigers manager Steve Bruce will take his side to Stoke on Saturday still seething over the decision that he feels cost the Tigers their chance of all but guaranteeing Barclays Premier League survival.
The result left Bruce still searching for one more win to reach 10 for the season - a figure he believes will be enough to stay up.
And Bruce admits he has been left frustrated after a campaign he claims has been blighted by refereeing inconsistencies.
“I will speak to (referees’ chief) Mike Riley again but I seem to have called him more this year than I have in my whole career,” he said.
“It is happening on too many big occasions. It has cost us at Tottenham, Swansea and West Ham and that for me is far too many.
“I know it’s a difficult job but we have to improve it and for me a bit of common sense has got to come back into it.
“I think referees are put under too much pressure. They can’t seem to referee like they used to - with a bit of common sense - and that’s the disappointing thing for me.”
Steve Harper will return to the starting line-up in place of McGregor, who is expected to remain in the high dependency unit of a London hospital for at least another four days.
Bruce added: “I went to see Allan yesterday and the kid is still in a lot of pain.
“Overnight the observations have been better but it certainly looks like he is going to miss the rest of the season.
“Allan is as brave as they come but he has taken a horrible knock to his kidneys and badly damaged one of them.
“We expect Allan to stay in the high dependency unit for another three or four days, then three or four more days in a normal ward.”
Bruce has recalled Eldin Jakupovic from his loan spell at Leyton Orient and the Swiss is expected to understudy Harper at the Britannia Stadium, while Bruce does not expect any more injury concerns.
Hull’s win over West Brom last Saturday had edged them closer to safety and Bruce remains convinced that one more win will be enough to put the seal on a highly successful season for his club.
But he expects a tough game against a Stoke side still looking to secure their own survival and heading into the game on the back of a thumping 4-1 win at Aston Villa last Sunday.
Bruce added: “We’re all looking to get to 37 or 38 points and there’s big games everywhere you look, and if we play like we did last Saturday, I think we’ll be fine.
“It’s difficult with back-to-back away games in the Premier League, especially when you’ve been down to 10 men for an hour, but the resilience and attitude was there for all to see the other night and you just have to dust yourself down and get on with it again.”