Brendan Rodgers' struggling side are languishing at the bottom of the Premier League table having lost five of their opening six games.
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Schmeichel made an unexpected move to French side Nice this summer after 11 years at the King Power Stadium, leaving only Jamie Vardy, Marc Albrighton and Daniel Amartey as survivors of the 2016 title-wining team.
Last week Leicester chairman Aiyawatt Srivaddhanaprabha revealed the club would have to curb their spending this summer to ensure they remain financially secure, which has left Rodgers unable to strengthen his side.
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Simpson was part of Leicester's title-winning side and insists the club's drop in form is down to the departure of key figures in the dressing room rather than the inability to bring in a host of new faces.
"As we know from pre-season, there has been stuff going on off the pitch and when you do lose your best players, and when I say best players I'm not just talking on the pitch, off the pitch as well," Simpson told talkSPORT.
"Kasper Schmeichel, he's been there for 11 years, the influence off the pitch as well as on it. I think he's been Leicester's best player over the last couple of years, making save after save.
"But it's just his influence in the dressing room. Sometimes when you lose that and you lose other players over the years like [Christian] Fuchs and Wes Morgan, that alone can hurt as well.
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Simpson has been keeping close tabs on his former side and despite the pessimism currently clouding the King Power Stadium, Simpson says one win could galvanise the players much like the situation Manchester United found themselves in last month.
"We all know you just need one win. Look at Man United after the Brentford game and they were rock bottom.
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"You just need that one win to get the lads going again.
"Aston Villa at home [on Saturday] is a must win. This game is where it's all to play for and I think they all know that."