Diego Simeone's men booked their spot in the Champions League final four with a 2-1 aggregate triumph over fellow La Liga title challengers Barcelona.
Atleti headed into Wednesday's second leg in Madrid with a 1-1 draw from the first fixture, and Koke's fifth-minute volley was enough to secure their progression.
Midfielder Gabi believes the success is a sign of Atleti's improvement in recent seasons, and he paid tribute the club's supporters for sticking with the team in difficult periods.
"We have been working these (past) years to be among the best and little by little we are (doing that)," he said.
"We dedicate the victory to the people who have supported us in difficult moments, who have suffered in recent years."
Next up for Atleti is a visit to relegation-threatened Getafe, with Simeone's charges gunning for a seventh consecutive Liga victory.
And Gabi has urged Atleti, who lead the Spanish top flight by one point from champions Barca with six games remaining, not to take the challenge lightly.
"The league is close and there are still six games where we have to fight," he added. "On Sunday we have a very important game against an opponent that is played down."
