Connacht coach Andy Friend said he was proud of the way his men fought back from 16 points adrift in the final quarter but was frustrated they didn't complete a shock victory in Paris.
His men secured a deserved bonus point and came agonisingly close to becoming the first side to defeat Racing 92 in the Heineken Champions Cup at La Défense Arena.
"I thought the fight was incredible. We said it at half-time, that we had been brave out there and that we needed a bit more in the second-half and that's what we got.
"It was frustrating that we couldn't nail it at the end there but very hard to be disappointed with the performance."
His side, badly missing the influence of Quinn Roux and Gavin Thornbury in the lineout, suffered a double blow in the opening half when they lost captain Jarrad Butler to a head knock and debutant flanker Seán Masterson to a knee injury.
They found themselves 19-3 down after 24 minutes as Racing powered their way over for tries from 20-stone tighthead Georges Henri Colombe, full-back Kurtley Beale and an acrobatic effort on his European debut from 21-year old winger Donovan Taofifenua.
But Connacht refused to crumble and they got themselves back in the game with the likes of centres Tom Daly and Sammy Arnold, full-back John Porch, loosehead Denis Buckley and brilliant lock Ultan Dillane leading the way.
Dillane was denied a try when scrum-half Teddy Iribaren forced a knock-on just short of the line, but a superb crossfield kick from Jack Carty, playing an advantage, was brilliantly taken by Matt Healy to score and make it 19-8 at the break.
Virimin Vakatawa had a try disallowed for an earlier knock-on nine minutes after the restart but the reprieve was short-lived for Connacht as former All Black Dominic Bird finished another good maul for the bonus point, with Iribaren's conversion making it 26-8 after 51 minutes and a rout was feared.
But Connacht refused to die and they got back in the game when Alex Wootton intercepted and ran from inside his own 22 after 62 minutes.
Tom Daly took over the kicking from Carty who had a knock and his conversion made it 26-15.
Beale had a second try ruled out after Teddy Thomas sent a forward pass in a simple two-on-one with Porch and Connacht hit back and were rewarded for a pounding of the home line when Conor Oliver got over four minutes from time.
Daly again converted and Connacht piled on the pressure in the dying moments knowing they were within sight of emulating their 2013 win in Toulouse.
But they were unable to close out the deal.
Tiernan O'Halloran couldn't reach a double hack and in the final play Carty's penalty to touch left them with too much to do from the 22 and Racing, runners-up in the competition three times in the past five years, were relieved to hold on.