Despite a 3-2 loss at Tottenham Hotspur, Atletico wrapped up a 7-5 aggregate win to set up a last-eight clash with Barcelona.
"Sometimes you don't need to say anything, the numbers speak for themselves," Simeone told reporters.
"It's a moment to be happy as a club, as a team, with the joy of our fans, who will celebrate this step towards the quarter-finals. When you get here, the road will be tough, as in previous situations where we reached the final."
Despite a three-goal cushion from the first leg last week in Madrid, Atletico made life difficult for themselves on Wednesday and needed goals by Julian Alvarez and David Hancko to ease their path as Tottenham threatened a comeback.
"The effort was enormous. The team didn't start well; the three-goal lead didn't help. We equalised, then it was 2-1, we equalised again, we had chances to close it out, and then came the final penalty. The draw was what we deserved," he said.
Barcelona went one better than Atletico in the last-16, scoring eight goals over their two legs against Newcastle United, seven of them on Wednesday.
The LaLiga leaders will be favourites in the quarters, but Simeone's side will take heart from their two-legged victory over Barcelona in the Copa del Rey semi-final.
"It will be difficult because we'll be facing the best attacking team in Europe, but we'll have the enthusiasm to compete," Simeone said.
After surviving a scare at Tottenham, Atletico will have little time to rest on their laurels.
They are away at Real Madrid in LaLiga at the weekend, and then face Barcelona three times in their next four games after the international break, once in the league and twice in the Champions League.