The Woking-based team enjoyed its best championship campaign in eight years last season, finishing third in the standings, whilst Ferrari endured a torrid campaign - its worst since 1980 - as the Scuderia finished in sixth.
Despite the threat the Italian team poses with a much talked about new power unit, Norris believes his team can aim to remain ahead.
Asked whether it would be more difficult to catch the top three or to keep Ferrari behind, Norris said: "For sure, to close the gap to the guys ahead.
"That’s always the more difficult part of it. It’s not like Ferrari are a miles better team than us. We have confidence in ourselves. We’re still an extremely good team.
“We’ve been on the fightback for the past few years, making good improvements and I think we’ve shown that lately, last year more than ever.
“I don’t think we can underestimate what we have been able to do in the past and what we can hopefully do in the future and that doesn’t mean we have to be always looking over our backs at what people can do.
“I think we can still just look forward to knowing we’re an extremely good team with extremely clever and talented people here at McLaren and we can just fight our own way back to the front."
McLaren's third-place finish last season came from a titanic battle with Racing Point, Renault and Ferrari, with AlphaTauri also threatening to break into the congested midfield.
Norris has warned the team cannot become distracted with attempting to beat a single team with others waiting to pounce.
“Racing Mercedes and racing Red Bull, that’s not where we are at the moment," he continued.
"It’s what we’re working towards and what we have been closing in on over the past few years.
“There’s going to be races where they [Ferrari] are quicker than us and hopefully more races where they are slower than us but it’s not just them, it’s every competitor on the grid which is able to beat us and be competitive against us so we’ll see.”
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