Diego Simeone's men booked their spot in the Champions League last four with a 2-1 aggregate triumph over fellow La Liga title challengers Barcelona.
Atleti headed into Wednesday's second leg at the Vicente Calderon with a slight advantage on account of their 1-1 draw at Camp Nou last week and Koke's fifth-minute volley was enough to secure their progression to the semi-finals.
Midfielder Gabi believes the success is a sign of Atleti's continued improvement in recent seasons and he paid tribute the club's supporters for sticking with the team in difficult periods.
"We have been working hard over these past years to be among the best and little by little we are doing that," the 30-year-old told reporters.
"We dedicate the victory to the people who have supported us in difficult moments, who have suffered at times in some of the hard years we have had recently."
Next up for Atletico is a trip to relegation-threatened Getafe, with Simeone's charges gunning for a seventh consecutive Liga victory.
Gabi has urged his side, who lead the Primera Division 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 often underestimated."