Kane, 24, was absent from England's friendlies against Germany and Brazil due to a knee injury he sustained in Spurs' 1-0 win over Crystal Palace prior to the international break.
England failed to score in either match, as they drew 0-0 against both sides. Jamie Vardy, Tammy Abraham and Marcus Rashford were used up front instead of Tottenham's number 10.
One-time England international Sutton claimed that England missed Kane on Tuesday night during their goalless draw against Brazil, delivering a very upbeat verdict on the powerful centre-forward.
"I would expect Gareth Southgate to start with three at the back in Russia but Tuesday night showed that he needs Harry Kane for this system to work. Against Brazil, England lacked a focal point," Sutton said.
"Kane is an intelligent, all-round footballer who loves playing alongside pace. He is superb at holding it, linking up and finding balls in behind for a pacy striker.
"Kane was always going to be a big part of England’s success at the World Cup — and his absence last night showed just how crucial he is to this team."
The former Norwich, Millwall and Leyton Orient loanee has been in sensational form for Mauricio Pochettino's side this season, scoring 13 goals in just 14 league and cup outings.
Now, Kane will be looking to continue his excellent form as he is expected to be declared fit to face north London rivals Arsenal at the Emirates Stadium on Saturday.