"To get all the way through to the quarter-finals in our Champions League debut season is a massive achievement", said Morgan.
Shakespeare felt Atletico's quality showed over the course of the two matches as the Premier League champions exited after a pair of hard-fought battles.
"We have to concentrate on points in the Premier League and climbing the table". We've spoken about being direct, playing Jamie and Riyad [Mahrez] off Leo.
Jamie Vardy (in blue) is consoled by Atletico manager Diego Simeone.
Leicester Citys Ben Chilwell vies for the ball with Atletico Madrids Fernando Torres (right) during the UEFA Champions League quarterfinal second leg at the King Power Stadium in Leicester, on Tuesday.
Los Blancos defeated city rival Atletico Madrid in the final both in 2014 and 2016.
Real are through to the semis for a seventh straight time and remain on course towards becoming the first team to defend the title in the competition in its current format.
"We had planned different scenarios in advance", he said.
But, having switched off in defence to allow Saul to nod in a crucial away goal after 26 minutes, Vardy's close-range finish proved their only tangible reward for a resilient second-half performance that merited at least a win on the night. "They made a lot of blocks on the line".
"What a great performance from our competitors tonight".
"Now we've had a taste of it, we want more", said Drinkwater.
The Spanish side went through 2-1 on aggregate after the two sides drew 1-1 on the night at Leicester's King Power Stadium.
Antione Griezmann, whose controversial first-leg penalty had given Atletico the edge, was a constant menace.
"It's been a wonderful experience for everyone at Leicester and they'll remember this for the rest of their lives", said former Foxes striker Tony Cottee on Sky Sports. "He caused plenty of problems in the area".
Leicester, meanwhile, has been banished back to Premier League midtable abyss. This season is ending with a more modest target: Survival.
"What we managed to do was nearly reinvent ourselves during the game".
England's last Champions League representatives went out with a fight exactly eight years to the day since Leicester began its dazzling ascent by clinching the third-tier title, with the exhausted players collapsing the turf at the final whistle after pressing with grit and directness.
Whether Leicester returns to the competition in the near future appears unlikely.
Clearly defined targets for the months and years ahead are needed to establish what sort of club Leicester hope to become. On the basis of that improbable and rapid climb, little will seem impossible for the years or generations to come at Leicester.
When their chance to strike came they produced a goal of stunning simplicity.