At one stage Connacht were 19-3 up thanks to a try-double from Niyi Adeolokun and Robbie Henshaw's effort, though Grenoble refused to give up.
Matt Healy also crossed over for Connacht but Denis Buckley's sin binning was to let Grenoble back in and foreshadow the cruel end to the game.
It's still all to play for in the Guinness PRO12 however, as Connacht sit in second place - with an eight-point buffer within the top four - before they welcome Munster next Saturday.
And Lam says pride is the overriding feeling after a difficult run-up to the Grenoble clash.
"We'll dissect the game, take what we can from it and look forward to Munster," he said. "We're looking forward to it in the Sportsground. We know we've got three games now to make the top four and we will get over this and get back into it.
"We're obviously very disappointed we didn't get the result, but I'm extremely proud of the guys.
"I sat in the changing room with the guys, I was obviously deflated and then I just started to reflect on the week we've had.
"We had a lot of last-minute changes, the travel, all of that, and I thought, 'Jeez, I'm proud of these guys.' A few guys out of position and we're down to the bare bones in a few positions.
"We'll be disappointed when we look back on Monday, because there were a couple of details we didn't nail and there's an opportunity when we're 13 points up and we didn't execute what we'd done at training."
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