Milan completed a swap deal with Juventus this month, bringing former Napoli star Higuain and defender Mattia Caldara to San Siro in exchange for Leonardo Bonucci returning to Turin.
Higuain scored against his old club Real Madrid in a friendly at the Santiago Bernabeu on Saturday, and has netted 16, 24 and 36 goals respectively in each of the previous three Italian top-flight campaigns.
Despite his potential importance in 2018-19, Gattuso wants to avoid his team becoming too dependent on the prolific Argentina international.
"We're going nowhere if we just rely on one player, even if it is Higuain. It's not enough," he told a news conference in the Spanish capital.
"In order to be credible, you have to do the work throughout the week, encouraging your team-mates and not insulting them. I've seen all of that since he arrived here."
Milan responded quickly to falling behind in Madrid, Higuain taking just two minutes to cancel out Karim Benzema's second-minute opener.
Goals from Gareth Bale and Borja Mayoral ultimately consigned the visitors to defeat, but Gattuso remains encouraged by what he has seen from his players.
"Last season our biggest problem was that we played some attractive football without bringing home a result, and now we've got the same regrets, so it's something we need to improve," he said.
"We've got to avoid conceding goals at the end of each half. It was a good performance overall, the side is in good shape and plays well. In general, I am happy, as we have strengthened this summer.
"It's true the gap with Juventus remains very large, but we are young and on the right track. If we continue like this, I don't think it'll take long to bridge that gap."