The Argentine is delighted to have seen off AC Milan, while Diego Costa feels that his side will put up a fight against any opponent whom they meet in the next round
Having won the first leg 1-0 at San Siro, Atleti ensured progression to the quarter-finals for the first time since 1997 at the Estadio Vicente Calderon, wrapping up a 5-1 aggregate scoreline.
Striker Diego Costa, who netted the only goal of the first leg, opened and closed the scoring to take his tally to seven in five matches in this season's competition.
Former Real Madrid midfielder Kaka had given Milan hope of a comeback by making the score 1-1 on the night but a deflected effort from Arda Turan and Raul Garcia's header put Atleti into a strong position before Costa made sure in the closing stages.
Simeone credited Milan for coming back into the match but hailed the performance of his players after the break, telling the press: "I knew that Milan could complicate things/ We started better than them in the first half and it seemed that we would go on and control the game after the first goal but they got back into it. However, my players were excellent in the second half."
"I am happy for the players and the fans. It is a night to remember. I am proud of sharing it with a team who try so hard in every single match.
He added on Sky Sport Italia: "Before their goal we had started to relax but afterwards we spent around 10 minutes without pressing, without getting the ball back and without calm. That was what we lacked at that time, the calm to cover the spaces and hold the field properly.
"I spoke to the team at half-time and after that I think everyone regained their calm. We suffered a little and Milan grew but, after the second goal, we started pressing higher up the field and that caused Milan more problems.
"We started strong and then had to change. I knew that if we kept the ball on the right then we could do well. It changed with Robinho, who wasn't coming back. It was dangerous for Milan to go on the counterattack so we had to hold on to the ball and beware of losing possession.
Costa was quick to thank the home support for helping Atleti to victory and insisted that there is no favourable tie in the last eight.
"We played very well as a team," the forward enthused. "We always have great support but, after [the way] we've played, we deserve the plaudits.
"We don't really want a particular opponent in the next round, all the teams that will be in the quarter-finals will be tough prospects."