The Catalan club continued their amazing start to the campaign, Lionel Messi's 83rd and 84th goals of the calendar year helping Barca move onto 40 points from 14 games this term.
"I'm very happy to be able to secure this record, but even more so by the performance of the players, how they played the game," said Vilanova, whose side's only dropped points this campaign came in the 2-2 Clasico draw with Real Madrid in October.
"It's fine to get these wins. We're happy, but we're more proud that today, in winning 5-1, we kept pushing, trying to press. If we continue to be strong, I'm sure we will win more games and surely will continue fighting for titles.
"Athletic play in a totally different way to other teams. They make it very difficult. Though the result is emphatic, it was not an easy game."
He added: "Of course there are things to improve, but the important thing is that we want to win and we have the ability to work hard.
"It is clear that we can lose games, but (working hard makes it) much harder to lose."
Vilanova, who stepped up from being Pep Guardiola's assistant in the summer when the former Spain midfielder resigned after winning 14 titles during his four years at the helm, felt it was too soon to compare his reign with Guardiola's.
"These four years are unrepeatable in everything that was done, the titles that were won and the evolution of the system of play," he said. " I feel very proud.
It is a very short time since then. One must (evaluate) further on."
Athletic boss Marcelo Bielsa acknowledged the Barca team had adapted to the new regime flawlessly.
"They have the same power, the same style, the same sense of constant balance from any ball in any sector of the field," the Argentinian said.
And Bielsa admitted his side had been second best on Saturday evening.
"We did not recover the ball well enough, and were not able to build attacks quickly without losing possession," he said. "But the big difference was that our attacks never thrived and every time we lost the ball led to a Barcelona attack."
Two goals in three minutes - from Gerard Pique and a deflected Messi effort - midway through the opening 45 minutes put Barca firmly in the ascendancy and Adriano added a superb third in first-half stoppage time.
Cesc Fabregas notched a neat fourth soon after the break and, after Ibai Gomez had pulled a goal back with Athletic's first noteworthy attack of the match, Messi rounded things off with a brilliant fifth goal.
Messi's brace left the 25-year-old needing just one more goal to equal Gerd Muller's record of 85 in a calendar year, set in 1972.
The win consolidated top spot in La Liga for Vilanova's team, who finished the day six points clear at the summit after Real Madrid saw off second-placed Atletico Madrid 2-0 in the late kick-off.