Saul Niguez's first-half header gave the visitors an away goal and put the tie out of Leicester's reach despite Jamie Vardy's second-half equaliser.
Atletico have now qualified for the semi-finals for three of the last four years and Shakespeare sees no reasons why the side cannot win the trophy for the first time in their history this season.
“Their history speaks for itself,” Shakespeare commented after the match.
“Finalists in two of the last three years and we knew what type of challenge to expect. After the first leg we felt we were in the tie and we had a right go but ultimately we've just failed at the last hurdle.
“I think they have been unfortunate in the last few years and we can see the quality they have in both games.
“They'll be tough opponents in the semi-finals but I don't see any reason why they cannot win it.”
Shakespeare also challenged his players to improve their league form next season so that they can seal a return to continental competition.
The Foxes, 12th in the Premier League, will not play in Europe next season and Shakespeare hopes this year's run will inspire his players.
“I hope the benefit is they want some more of it. They are very disappointed but can be proud of what they've achieved,” he said.
“As a football club we can be proud of how we've conducted ourselves. All players want to play at the highest level and the Champions League is the highest level but we have to get back to winning ways in the Premier League now.
“The feeling is one of disappointment to go out but I'm immensely proud of the performance. We got the goal and couldn't quite get the breaks which was needed to get more.”Reuse content