Hodgson watched on at a half-empty Wembley on Wednesday as England toiled to a 1-0 friendly win over Norway, courtesy of captain Wayne Rooney's second-half penalty.
After a dismal World Cup campaign that ended with a group-stage exit, England's performance was hardly one to reignite enthusiasm among disillusioned fans.
Hodgson felt Norway had approached the game with a focus on defence, but he believes Switzerland will be under pressure to attack when the two sides meet in Basel.
"Switzerland will need to beat us, if anything we might be Norway on Monday," he said.
"We might be pushed back and can't attack and dominate for long periods, as we did [against Norway].
"I don't think the mindset of the Swiss team, playing us in Basel, will be the same as the mindset of the Norwegians."
When it was put to the manager that Rooney's penalty was one of only two shots on target, Hodgson appeared irked by the suggestion.
"Don't give me that one. Two shots on target? What about all the ones they threw themselves in front of.
"Don't hit me with statistics. When we had that much possession and you talk about two shots on target?
"We're not scoring a lot of goals, but we're not playing against teams who come out against us a lot. This team will score goals. They'll score goals.
"Rooney will score goals, [Daniel] Sturridge will score goals, [Danny] Welbeck will score goals, [Raheem] Sterling will score goals."
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