The London club went down 2-1 due to a late goal from Atletico Madrid's Diego Forlan just minutes before the match would have gone into penalties and Davies admitted that a loss like that was hard to take.
"Getting so close to penalties we were hanging on a little bit. We were hanging on and looking to try our luck there. It's a shame to get so close but once we get home after a few days we'll feel like we achieved something but now it is very painful," he told Five.
"Scoring in a big final I'll be very proud in years to come but now it is really hard.
"We were so close but we must congratulate Madrid."