The Tottenham Hotspur striker scored a brace as the Three Lions secured a last-gasp 2-1 win over Tunisia in their first game of the competition on Monday night.
Shearer, one of England's most prolific forwards and the winner of the Euro 1996 Golden Boot, believes that Kane will have been spurred on by the goalscoring performances of some of his peers in Russia.
"I can't stress enough the importance and confidence of Kane," Shearer told BBC Sport. "He'd have been looking at [Cristiano] Ronaldo and [Antoine] Griezmann over the last few days.
"The manager (Gareth Southgate) gave him the armband because he's the go-to player. The goals will have given him great confidence tonight.
"There's no doubt [Kane will be thinking about Golden Boot] - he would have been desperate to get off to a goalscoring start."
Kane now has 15 goals in 25 appearances for England.