Jamie Vardy's goal earned a 1-1 quarter-final second-leg draw against Atletico Madrid but the Foxes went out 2-1 on aggregate.
- [They'll be hurting, but Leicester will always have the night they gave Atleti a huge fright]
- [Atletico end Leicester dream despite Vardy strike]
Saul Niguez's first-half header grabbed a crucial away goal for Atletico and they held on despite a second-half rally from the hosts on Tuesday.
Shakespeare was proud with the performance but with no European football next season he challenged his players to return Leicester to the competition in the future.
"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."
And after helping guide the Foxes to the quarter-finals after replacing Claudio Ranieri in February the boss would welcome the chance to talk about his future before the end of the season with his contract as manager expiring in June.
"It's not in my hands. It's in the club's hands, I've said we'd sit down at the end of the season, I'm more than happy to do that before if it arises but the contract says until the end of the season," he said.
"I've enjoyed it, pitting your wits against one of the best managers in the world, one of the best sides in the world.
"Now is a time to reflect and I'm sure at the end of the season I'll be able to reflect on my own performance as well as the club's."
Read the full article on eurosport.co.uk: Craig Shakespeare: Now let's get Leicester back into Europe