The striker was pipped to the Premier League's top scorer prize by Liverpool star Mohamed Salah last term but made amends by claiming the World Cup Golden Boot thanks to his six strikes at Russia 2018.
Kane has faced criticism for what have been perceived to be lacklustre performances at the start of the 2018-19 season, although he broke his notorious August duck by netting in wins over Fulham and Manchester United.
Spurs boss Mauricio Pochettino has labelled criticism of his star striker "rubbish" and Eriksen feels the considerable goalscoring demands placed on Kane are becoming too much.
"Everyone expects him to score three goals every game," Eriksen told the Independent.
"As a team we know we have to feed him, but in a team that is losing it is very difficult to score goals, even one that keeps creating chances.
"I know Harry wants to score more, and so do the rest of the team. At the end of the day it doesn't matter who is scoring and who is not scoring. It's about winning games."
A lack of signings in the transfer window, coupled with many stars featuring at Russia 2018, are cited among possible reasons for a stuttering Spurs start to the new season.
"We are not tired after the World Cup. Everyone has had near enough the same break," Eriksen added.
"Of course we are unfortunate we had so many players going so far in the tournament, which meant they started their pre-season later.
"But our performances have had nothing to do with tiredness. And personally, I haven't felt tired.
"There is no better place to put things right than at the San Siro. It's the perfect stadium to play in.
"And there will be no better way to start a Champions League campaign than with a win at the San Siro. It's going to be an exciting game."
Reports have suggested contract talks between Spurs and Eriksen have reached an impasse, with the Denmark international's deal expiring in 2020.
"I am just focusing on football," Eriksen added. "I leave the talking to someone else. But I am very happy where I am."