Atletico held a 1-0 advantage from the first leg and they doubled their lead after 26 minutes thanks to a superb header from Saul Niguez.
"The whole club, from the supporters to the players to the owners can be immensely proud", said Shakespeare. "The players should be proud, but they're ultimately disappointed to go out". We're a squad that believes we can do things some people probably didn't think we're capable of, but we just keep pushing ourselves on the training field and out on the pitch.
Danny Drinkwater wants another crack at the Champions League with Leicester City and insists the club have nothing to fear from Europe's elite.
Speaking as he analyzed his former club's Champions League quarterfinal defeat to Atletico Madrid, he said: "I am ready".
With six games left and 18 points up for grabs - they have 37 in 12th place now - Leicester's players are targeting a finish in the top half of the table.
Leicester City shocked many, as the Foxes were the last remaining English side in the Champions League.
With Atletico qualified, there will be at least one Spanish side in Champions League semi-finals for the 10th season in a row.
Leicester's Jamie Vardy's 61st-minute goal canceled out Niguez's 26th-minute strike in the second leg of the quarter-final on Tuesday night but Atletico's 1-0 win plus an away goal here gave them a comfortable 2-1 win.
The victory at the Santiago Bernabeu Stadium put Madrid into the semifinals for the seventh straight season and kept alive its hopes of becoming the first team to retain the Champions League title since the competition's new format was created in 1992.
In reaching the last eight in their maiden Champions League campaign, Leicester bettered the competition debuts of Manchester United, Arsenal and Manchester City (since the tournament's 1992 rebrand).
"It was nearly a pleasure to compete against them", Simeone said through a translator. I'm pitting my wits against the best in the world.
"Atletico Madrid are a big force in Europe and we pushed them all the way". I'm more than happy to do that before if it arises but the contract says until the end of the season.
Shortly after Griezmann's electrifying run nearly brought a second for the Spaniards, Leicester got their lifeline.
Chilwell's shot at the goal was blocked by a flying Stefan Savic but deflected right towards Vardy, who rifled it home from close range.
Real boss Zidane said: "We played 120 minutes and in the end, some players have finished a bit worse for wear". The effort and the commitment we showed second-half, it had them rattled.
"It was just unfortunate we didn't get the result we wanted".
Simeone said: "I'm full of emotions, full of pride for the performance of my team".
After a stirring pre-match introduction for both teams, the home fans roared on their team as they looked to make up the one-goal deficit from the first leg.