The Premier League champions are 2-1 behind in the last-16 tie ahead of Wednesday's (AEDT) second leg at the King Power Stadium, but Shakespeare believes Jamie Vardy's away goal gives them every chance of progressing.
And Shakespeare is ruling nothing out if Leicester can secure their place in the last eight of the competition.
Asked if Leicester can win the Champions League, Shakespeare said at his pre-match media conference: "Why not? We are in it. We have to try and be competitive every game.
"There is a great opportunity for us [against Sevilla] and we will give it our best shot.
"We have to compete for the 90 minutes or extra time. We have practiced penalties and we try to leave no stone unturned. By the way the penalties were good!
"We knew by getting the away goal it gave us a great opportunity. We give ourselves a great chance.
"It makes it very interesting. It will be a special occasion and the atmosphere will be electric.
"We are not going to be open but I want to play on the front foot. Hopefully I will stay calm so the players are not overemotional, but of course I will be excited.
"Sevilla have huge experience in Europe. I will expect them to play the same way. They have talented players. It is more about the players than me pitting my wits against [Jorge Sampaoli]."
The Sevilla clash is the first game since Shakespeare was confirmed as Claudio Ranieri's replacement until the end of the season on Sunday, with the former assistant boss having previously been in caretaker charge.
"I'm still settling in," he said. "I'm delighted and comfortable with it being until the end of the season.
"I understand the challenges that are ahead. Some massive ones and none more so than Tuesday night.
"I'm not looking beyond this season. We have massive games coming up and we have to focus on that. We will have plenty of time in the summer to take stock and evaluate things then.
"For me how you treat and talk to people is so important. Man management is a real big component, of course there will be decisions that have to be made but as long as you explain it to people players will be happy with that."
Shakespeare has not spoken to predecessor Ranieri since his appointment was confirmed.
"We have not spoken since," he said. "We will probably be in contact in the future – I have no problem with that."