Leicester are 15th in the league and sit just six points above the relegation zone with a trip to Arsenal due later on Wednesday.
"At the moment, he's banging in the goals and we need that to continue from now to the end of the season," Shakespeare told British media.
"I'm reluctant to say he's back to his best, as I want more from him, but his goalscoring of late has been very good.
"At the moment, you see a player full of confidence and full of running, we need a Jamie Vardy threatening defenders, getting on the shoulders and being a goal threat as well."
Leicester endured a horrid start to the season and parted company with manager Claudio Ranieri in February.
Shakespeare said the mental toughness of players like Vardy has been instrumental in helping Leicester climb to within touching distance of safety.
"I think all players will go through peaks and troughs, they have that and they have to stay mentally tougher which Jamie did," he added.
"It's about rolling your sleeves up and making sure you turn those indifferent performances into good performances and you see the Jamie that we're seeing out here at the moment, playing full of confidence but a goal threat as well."
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
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