The visitors had celebrated progression through to the last eight of the Europa League in midweek, but a Diego Godin own goal and Michael Pereira strike left them trailing to Mallorca.
The dismissal of Ivan Ramis gave Atletico hope of a comeback, but a missed penalty from Falcao proved costly with his later goal not enough to rescue Diego Simeone's side.
Atletico had the first glimpse of goal after 14 minutes. A free-kick from Eduardo Salvio was headed goalwards by Mario Suarez but kept out by the fingers of home goalkeeper Dudu Aouate.
Chances were harder to come by for Mallorca, but they threatened to take the lead six minutes before the interval when Jose Nunes headed a corner from Sergio Tejera inches over the bar.
They were gifted the opening goal two minutes into the second half, however. Pablo Caceres' cross into the box found the feet of Gonzalo Castro, who saw a left-footed shot sliced into his own net by Godin.
Atletico had barely had time to register that goal when they found themselves 2-0 down. Victor set up Pereira with a neat pass which the midfielder lashed into the bottom left corner from 18 yards.
Mallorca's luck looked to have changed after 53 minutes, though, when Ramis was given his marching orders for a handball in the area.
Falcao stepped up to take the resulting spot-kick but Aouate got down to push the ball away.
The Atletico striker fared much better after 66 minutes, beating Aouate with a fantastic 20-yard lob which left the home goalkeeper stranded.
That sparked the visitors to life and they should have been level two minutes later but Fran Merida's left-footed strike hit the post.
Dudu Aouate then kept Mallorca in front with a fingertip save to keep out a close-range effort from Adrian, and Godin had the chance to make amends for his earlier blunder but put a header over the bar two minutes from time.