Atletico have reached three European Cup finals in their history — two during Simeone's near 15-year tenure — but have never lifted the continent's top prize. They are the only team to lose three finals without having won the competition.
This season has offered little domestic comfort, with the club fourth in LaLiga, 25 points behind leaders Barcelona and effectively out of the title race since January.
Defeat on penalties to Real Sociedad in the Copa del Rey final less than two weeks ago has left the Champions League as Atletico's sole remaining shot at silverware this season, and they could be heading for five trophyless seasons in a row.
Yet Simeone was in no mood to look back at past failures after defeats by Bayern Munich (1974) and Real Madrid (2014, 2016) in the final of Europe's elite club competition.
"There's no pressure, there's a sense of responsibility, and there's a special sense of anticipation," he told a press conference on Tuesday.
"At the end of the day, it's a football match and the players are the ones who decide the outcome. We have to prepare well. We want to play the game we've envisaged and take the match to a stage where we can cause Arsenal problems."
Asked whether the competition owed Atletico something after three final defeats, Simeone said: "We're all human. If you ask us, everyone has a different opinion. But a competition doesn't owe anyone anything.
"Things have to be earned and achieved. You have to work hard, go out and get them and hope Lady Luck is on your side."
The Argentine pointed to Atletico's approach in recent knockout ties as their greatest asset.
"What we've been doing in the knockout stages, whether in the (Spanish) Cup or the Champions League ... Playing with intensity, with our style of play, with our attacking initiative. That's how we'll go about it," he said.
For a club chasing a first Champions League crown, there is a temptation to dream but Simeone prefers deeds to daydreams.
"Dreaming is all well and good, but reality is what happens on the ground. Reality is what we do and what God wills. That's how we behave," he said.
"We're in another semi-final. It's extraordinary to reach it for the fourth time in 14 years. It's incredible.
"That faith, that excitement, that infectious spirit will do us a world of good. We're facing a tough match but we're going there full of hope."
Follow the first leg between Atletico Madrid and Arsenal with Flashscore!
