Last season's Champions League runners-up went 2-0 up in the first half courtesy of goals from Saul and Antoine Griezmann, before Karim Bellarabi pulled one back for the Bundesliga side early in the second half.
Further goals from Kevin Gameiro and Fernando Torres as well as an own goal from Stefan Savic ensured Atletico return to Spain with a two-goal lead, though, and Simeone was delighted with his side's outing.
"I can go back to Madrid with a big smile on my face," Simeone told reporters.
"We thought before the game that, if we attack down our left side, we would cause their right-footed defenders problems. That is exactly what we did.
"Leverkusen fought their way back into the game in the second half, but overall it is a very satisfying evening for us. It is important to have belief when you play away from home, and I thought we had that in abundance.
"We could even have won by a higher margin, but their goalkeeper pulled off two outstanding saves to deny Griezmann. Gameiro has never had a better game for us. Griezmann did very well too.
"We did well, but the important thing for us is that we continue to improve. It is important not to concede that many goals at this stage of the tournament, so that is something we need to work on.
"Leverkusen have nothing to lose in the second leg, so we need to be careful. Even so, we can be very pleased with our efforts."