David Moyes felt a draw was the right result after an own-goal from Tomas Soucek cost him victory in his 1,000th match as a manager.
But luckless substitute Soucek inadvertently headed a late cross inside the near post to leave the Hammers with just a point.
Nevertheless, Moyes was satisfied to see his side, who were below par in the first half, still well clear at the top of Group H following three wins and a draw, and destined for the knockout stages.
“I think on reflection a draw is the right result,” said Moyes. “Genk started better and we needed our keeper to make some good saves.
“In the end we got two goals and it looked like it would be enough but for the own-goal. Lots of credit to Genk.
“I’d slightly altered things, and I changed it round again after 20 minutes and after that some of our football was really good, we just couldn’t find the finish.
“I look at it that we’ve qualified, and the other part of it is we’re still new to this. We are trying to keep players fresh for the Premier League, so somewhere along the line it was going to get bumpy. And Genk made it bumpy.”
West Ham fell behind after only four minutes to the first goal they had conceded in the competition.
They were caught napping by a ball in behind, which Joseph Paintsil raced onto and fired across Alphonse Areola, who got a hand to the shot but could not keep it out.
The Hammers levelled on the hour when Manuel Lanzini sent Vladimir Coufal overlapping down the right and his pull-back was swept home by Benrahma.
With 10 minutes remaining Benrahma scored a fine solo goal, nudging the ball one side of defender Mujaid Sadick and skipping past him on the other before poking home at the near post.
“I thought Said played well tonight, he did a lot of good things which in recent games I’ve not been so sure, and getting a couple of goals will help him, so good on him,” added Moyes.
But Benrahma was not to be the match-winner as, with three minutes to go, Soucek inadvertently glanced a cross from Genk substitute Angelo Preciado past Areola to deny Moyes victory on his big night.
On his milestone match, Moyes said: “I’ve not really taken that in yet. As a manager you’re just thinking about the last minute so I’ll probably reflect on it later.
“But it’s quite hard to believe that I’ve got there and it’s a moment I’ll always remember, an away game in Europe. And the game will always be remembered for when Tomas Soucek scored an own goal.”
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