The 24-year-old opened the scoring in Monday night's Group G match inside the first 11 minutes before Ferjani Sassi netted a controversial equaliser from the penalty spot.
Merson, who represented England at the 1998 World Cup, believes that Kane's all-round play was not good enough and needs to improve if the nation is to go far in the tournament.
"If I'm being honest - and I'm one of his biggest fans - I thought he was poor," the 50-year-old told Sky Sports News.
"He scored the two goals, but he brings more to the team than that. He's not a Gary Lineker, who would touch the ball twice and score two goals and that's what he brought to the team.
"They need Harry Kane to hold the ball up, get involved and bring other players into the game. I don't think he did that. That's being a little bit too critical and I'm thinking ahead to the knockout stages."
England's next match will be against Panama on Sunday.