The US had a seemingly unassailable 10-6 lead going into the final day, but were pegged back by a superb European display that saw them complete a record-equalling comeback.
Mickelson was one of the Americans to lose his singles encounter, and admitted that the defeat still hurts.
"I don't know what happened Sunday. I'm still licking wounds from that. It still stings. It's one of the toughest, most difficult losses I've ever had in my career," he told ESPN.
"Individually, that and the Winged Foot US Open loss (in 2006) have stung the most. This one still hurts. I really thought we were going to get that win.
"When we had to be accountable to our team-mates and to our country and the people that are pulling for us and supporting us in the United States of America, we just felt so, I mean, we still do, we feel so down and disappointed about it."
Europe eventually won the Cup 14.5-13.5 in the penultimate match of the day.