Irish reinvigorated their campaign with a superb bonus point win in Paris last week, but they undid that work as Racing grabbed their first win.
The kicking of visiting fly-half Jonathan Wisniewski proved the difference as he landed three penalties, three drop goals and converted Sereli Bobo's try.
Irish had their own goal-kicking ace in wing Tom Homer, who booted four penalties and the conversion of hooker David Paice's last-gasp touchdown which at least gave the Exiles a losing bonus point.
But the loss leaves Booth's side five points behind Pool Two's joint leaders Cardiff Blues and Edinburgh with two matches left to play.
"I never accept it (failing to qualify) until it is not possible but, if it was hard enough before, then it is hard enough now," Booth said.
"We didn't take our chances and we were unable to control the tempo of the game. Those two points were the reasons why we are talking about it now (as a losing team). How much slow ball did we have?
"You have to give Racing credit for controlling our environment.
"When you stress them, you have to be clinical and we weren't clinical. It is all about getting to the red zone and getting something from it. You have to control the scoreboard.
"They got an intercept try when we were forcing the issue when we didn't have to."
Booth remains hopeful of progressing, though, adding: "We have always said how evenly positioned the group is. It has been the nature of this competition and the group and it reminds you that, if you perform at home, the easier it is."
Racing's former Exeter centre Josh Matavesi was proud of his team, who bounced back from last weekend's home humbling to grab their first win and keep their own slender hopes alive.
"Last week, they came at us and played us off the park and we had no answer," he said.
"This week, we took them on, although you cannot give them an inch.
"I think the boys fronted up well and showed courage. We had to prove a point because we have a big game coming up against Agen before Christmas."
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