Spurs suffered a heavy defeat at Emirates Stadium on Saturday but Villas-Boas was proud of the way his men battled after Emmanuel Adebayor had been sent off against his former club in the 18th minute.
And he says there were so many positives to take from the performance that Tottenham should be able to bounce back quickly.
"When you are poor, it can do damage, but when you play like this I don't think it can," the Tottenham manager said.
Santi Cazorla, Theo Walcott and Jack Wilshere carved open Tottenham's back four with ease and Villas-Boas admits his side's defensive shortcomings must be addressed.
"We are a good attacking side but we have been conceding a couple of goals," Villas-Boas said. "We understand that we have to do better.
"But we suffered three in the first half, we suffered two in the second half, with one player less.
"There was attacking volume for both sides. Arsenal were efficient in their chances and we weren't as efficient in ours."