Atletico Madrid 2-0 Celtic
Celtic's Europa League group campaign opened with defeat as they failed to test Atletico Madrid in Spain.
Falcao took advantage of some slack marking to head the home side ahead from a third-minute corner.
Gary Hooper had an early effort blocked and, early in the second half, Ki Sung-yueng's powerful drive had to be tipped over the bar by Thibaut Courtois.
Atletico put the game beyond Celtic when Diego ran on to Arda Turan's cut-back to shoot home.
Celtic manager Neil Lennon can only dream of a transfer budget that could attract the likes of Falcao and Diego and the home side always appeared to have another gear as they built on the perfect start.
Not for the first time on their recent European travels, Celtic conceded a soft early goal.
A good sliding challenge from Charlie Mulgrew gave away a corner and Colombian striker Falcao ran between two defenders to powerfully head Diego's delivery home from 10 yards.
Celtic had a great chance to draw level just a few minutes later when Hooper exchanged swift passes with stand-in skipper Beram Kayal. However, Atletico goalkeeper Thibaut Courtois rushed out to block as the striker got the ball caught under his feet.
With the visitors camped deep in their own half, Atletico were able to patiently ping the ball around but were restricted to shots from distance by some stubborn, well-organised defending.
The busy Turan fizzed an effort narrowly wide and Diego had a fierce strike beaten away by Fraser Forster.
Celtic began the second half in positive fashion, with a 35-yard thunderbolt from Ki producing a good fingertip save from Courtois.
Mulgrew then curled a free kick wide but, just as Celtic appeared to have established a foothold in the game, they fell further behind on 68 minutes.
Turan skipped away from Mark Wilson and got to the bye-line before pulling the ball back for Diego to find the bottom corner of the net with a well-placed first-time strike.
Buoyed by the cushion of a second goal, Atletico rediscovered their earlier zip and Turan was denied a goal when Forster did really well to push the Turk's curling shot onto the junction of crossbar and post.
Celtic responded with strikes from Joe Ledley and Kayal, both rising too high to trouble Courtois.
Former Arsenal man Jose Antonio Reyes almost set up a late goal for the home side after a burst into the penalty box but Forster got a hand to Turan's shot and Kelvin Wilson was on hand to hack the ball clear as it rolled towards the goal.
Atletico Madrid: Courtois, Perea, Godin, Miranda, Antonio Lopez, Turan, Mario Suarez, Diego (Tiago 84), Gabi (Adrian 70), Koke (Reyes 56), Falcao. Subs Not Used: Sergio Asenjo, Salvio, Pizzi, Dominguez.
Goals: Falcao 3, Diego 68. Booked: Gabi, Mario Suarez.
Celtic: Forster, Mark Wilson (Matthews 80), Kelvin Wilson, Loovens, Mulgrew, Kayal, Ki, Ledley (Bangura 78), Hooper, Forrest (Commons 83), Samaras. Subs Not Used: Zaluska, George, Filip Twardzik, Wanyama.
Booked: Kayal, Loovens.
Ref: Peter Rasmussen (Denmark).