The 53-year-old will start his reign with a monumental clash against Sevilla on Tuesday night at the King Power Stadium as the Foxes attempt to reach the UEFA Champions League quarter-finals having lost their last-16 first-leg 2-1 away from home.
"If we think that a one-goal advantage will qualify us, it's a mistake", the Argentine manager said.
"Let's see what they're like when it's minus three back in Leicester", said Vardy before Shakespeare's appointment.
"We're definitely still in it, we'll look forward to the next leg and hopefully we can get through".
Shakespeare has been of the Foxes' coaching staff for seven of the last eight seasons.
"The team (Leicester) is now back to being as unsafe as they were previous year".
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At the same time, Sevilla's refreshing drive for the Liga title hit alarming roadblocks with two draws so undistinguished that their demanding fans booed them off the pitch on Saturday after the home match against lowly Leganes finished 1-1.
Shakespeare has overseen 3-1 victories over Liverpool and Hull City since taking over from Claudio Ranieiri who was sacked last month by the club's Thai owners less than a year after taking the Foxes to an unlikely EPL title last season. We have practiced penalties and we try to leave no stone unturned. "We always knew the team would be in good hands when we asked him to take charge a fortnight ago", said the club's vice chairman Aiyawatt Srivaddhanaprabha.
He has initiated the positive response we hoped change would bring'. "We were all very happy to see him get it short term, I'm sure it would be the same reaction longer term".
"We have massive games coming up, we have to focus on that".
Even so, Sevilla were so superior in the first game between the two sides that it's hard to see them not getting on the scoresheet in this encounter at the King Power Stadium.
Defensive midfielder Nampalys Mendy will miss the Sevilla game due to a knee injury.