The visitors had the better of the chances in the first-half, but had to ride their luck in the second as Getafe were denied a strong claim for a penalty before Mario Suarez was sent-off for a second yellow card.
Thibaut Courtois then had to make a fine save from Borja Fernandez with six minutes remaining before Diego Godin was also given his marching orders for a second bookable offence in stoppage time.
The draw means Atletico have now won just one of their last five league games and manager Diego Simeone accepts they are struggling to reproduce their early season form.
"The season is very long and the opponents start to know you and look for solutions," he told a press conference.
"We won in Pamplona (against Osasuna), drew against Valencia and here. We would like to continue improving and it is true that we have not been as efficient as we were earlier in the season."
Atletico's dip in form has also coincided with Radamel Falcao scoring just once in the last five outings, but Simeone defended the Colombian's record so far this season.
"We know Radamel is an important player in front of goal and his numbers are incredible.
"He has 22 goals with eight games to go, which is only two less than he had last season. I don't think this has happened very often.
"I hope we will always have a striker that assures this number of goals."
Falcao did though uncharacteristically miss a great chance to give Atletico the lead early on when he prodded wide from Diego Costa's cross.
Atletico were fortunate after the break though as referee Carlos Delgado Ferreiro somehow judged that Godin's trip on Adrian Colunga took place just outside the box despite contact clearly being made well inside the area and Barrada sent the resulting free-kick inches wide.
Simeone's men weren't so lucky minutes later as Suarez saw a harsh second yellow for handball. However, despite the man advantage, Getafe struggled to create chances and their best effort came when Borja let fly from 25 yards but Courtois showed strong hands to parry the ball to safety.
And a scrappy game was summed up when Godin was shown also shown a second yellow card in stoppage time for catching Alvaro Vasquez as they contested a high ball.
Valencia kept up their pursuit of fourth place as Jonas' injury time header handed them a 2-1 win over 10-man Valladolid.
Mikel Balenziaga's own goal had given the hosts a half-time lead and Henrique Sereno was then dismissed after bringing down Roberto Soldado inside the area 11 minutes after the break.
But Soldado's penalty was saved by Dani Hernandez and Oscar Gonzalez looked to have rescued the visitors a point with a lovely finish in off the underside of the bar 19 minutes from time until Jonas' late intervention.
At the bottom Celta Vigo remain in the bottom three as they lost 2-0 at home to Rayo Vallecano.
Piti and Andrija Delibasic got the goals for Paco Jemez's side to leave Celta still three points off safety with eight games remaining.
And Osasuna are also still in the relegation battle as they too lost 2-0 at home to Espanyol.
The hosts were left to rue Kike Sola's incredible first-half miss as goals after the break from Hector Moreno and Mubarak Wakaso moved Espanyol up to 11th.