The Argentine says the Premier League visitors made it difficult for the hosts, but was delighted that he could help fire the Partenopei through in the Europe League
The Partenopei, who were held to a 0-0 draw at the Liberty Stadium last week, were fired ahead by Lorenzo Insigne early on but Jonathan de Guzman's leveller left the Stadio San Paolo unsettled.
However, the former Real Madrid striker popped up to score his 20th goal of the season in a Napoli shirt, with Gokhan Inler bagging a complementary third for the hosts in stoppage-time.
Higuain suggested that a 3-1 win on the night was a little flattering for Rafa Benitez's men and stressed the result is more important than his goalscoring performance.
"We knew it was an important game and it was a difficult struggle," the Argentine, 26, told Mediaset Premium. "Swansea forced us to wait over 70 minutes to secure the win.
"I want to thank my team and our fans for helping us to gain this qualification. We started the game well, though after the equaliser we fell back a bit, but we can be satisfied with the outcome.
"It's more important that the result was good than getting a goal, I'm happy with that."
Napoli will face Porto in the last 16 of the Europa League, after the Portuguese giants defeated Eintracht Frankfurt on away goals on Thursday in a 5-5 aggregate result.