Atletico are joint top of La Liga with Barcelona after picking up 50 points from a possible 57 in the first half the season, while in Europe they stormed through the group stages with 16 points out of 18 - a tally matched only by bitter rivals Real Madrid.
They will now face stuttering Italian giants AC Milan in the last 16 of the Champions League next month, but despite chasing honours in three fronts, Simeone has dismissed any suggestion the Copa del Rey will take on secondary significance for the Rojiblancos.
Simeone, who led Atletico to the cup title last season, said: "Since I was a small kid I've always wanted to win, even at table football.
"The cup is a competition that has given us a lot of joy and we respect it like we respected the friendlies in Peru and Argentina. We have this characteristic, this desire.
"We only play to win in the best manner."
The Argentinian was speaking ahead of Tuesday's last-16 second leg against Valencia at the Vicente Calderon, where the two teams are locked at 1-1 following the first meeting.
Atletico had looked set to sneak a narrow advantage thanks to Raul Garcia's second-half header and some brilliant saves from Thibaut Courtois but Helder Postiga nodded home a stoppage-time equaliser to earn Valencia a draw.
Simeone added: "They have to score. I imagine that they are going to try and play the way they did in Valencia. In the last 20 minutes they were very good. It will be a difficult game."
Whereas the outcome of that tie remains in the air, there appears little doubt Barcelona will be gracing the quarter-finals as they hold a 4-0 lead heading into their trip to Getafe.
Getafe have also lost their last four matches in the league, but captain Rafa Lopez is not giving up hope of causing a massive cup exit against 26-time winners Barca.
He said: "It's very difficult to turn it around, but we're going to give it everything to try and do it. Barcelona are one of the best teams in the world but we're not going to give up."
Real Madrid, who were upset on home soil in last year's final by Atletico, are also favourites to go through against Osasuna as they hold a 2-0 lead, although Carlo Ancelotti's men will still need to be wary.
Osasuna have won their last two league matches and have held both Real and Barcelona to draws at home this season.
In this week's other last-16 second legs, Real Betis will be hoping for some cup cheer to ease the pain of a miserable league campaign when they take on Athletic Bilbao.
Betis' 2-1 home defeat to Osasuna on Sunday left them five points adrift at the foot of the Primera Division standings but they hold a 1-0 lead in the cup as they head to San Mames on Thursday.
Espanyol, meanwhile, will be looking to avoid a shock as they hope to overturn a 1-0 deficit at home to second tier Alcorcon on Wednesday, while the other three ties are all level after the first legs - Villarreal-Real Sociedad and Levante-Rayo Vallecano finished goalless while Almeria drew 1-1 with Racing Santander.