The Premier League champions are the last English club left in the competition and face Atletico Madrid in their quarter-final first leg in Spain on Wednesday.
They are underdogs ahead of the game at the Vicente Calderon, despite having knocked out Atletico's LaLiga rivals Sevilla in the last 16, and are minnows in Europe.
Shakespeare said: "We have enjoyed it but make no mistake we're there to compete and not to make the numbers up. These players deserve this opportunity and we aim to keep that going.
"You have to pinch yourself but these are the nights you look forward to. It's a traditional ground. It gives you a little tingle.
"But I'm on this side now, you have to enjoy it but to enjoy it you have to make sure you get a result.
"In terms of life experience you use them as you go along, you have new ones and this is for us in the Champions League this season."
Kasper Schmeichel, who had a spell with Notts County in Sky Bet League Two between 2009 and 2010, also insisted he was inspired.
Schmeichel will captain the side with Wes Morgan out injured and said: "When you look at the DNA of our team, the type of characters, the journeys everyone has been on - lower leagues and rejection - these are the kind of nights, when you are playing League Two and watching the Champions League on TV, you were working for."
Shakespeare still had to field questions about former manager Claudio Ranieri after the Italian hinted he was betrayed.
Ranieri was sacked in February and broke his silence on Sky Sports' Monday Night Football - clearing the players of blame but still said "maybe it could be somebody behind me" although Shakespeare reiterated the pair never had an issue.
"Free speech is there for anyone, I don't have a problem with that. I'm quite comfortable in my own conscience," said Shakespeare.
"There's never been any arguments or hard feelings. That's my side of it. It was good to see him enjoying his football as he did. I thought he came across really well."
Atletico are third in LaLiga and have lost just four games at home in all competitions this season but boss Diego Simeone is wary of Jamie Vardy, who has scored seven goals in his last 10 games.
He said: "I like him, I really rate him as striker. He is the kind of powerful striker Atletico have had. He also gives the team a lot of depth, and makes life really difficult for defenders to get ball out.
"He is very dangerous and if we make any mistakes, he will penalise that."