The Eagles dominated for large periods in Amsterdam, particularly in a first half in which they squandered numerous chances to take the lead.
Fernando Torres made them pay by putting Chelsea in front on the hour mark and although Benfica equalised through Oscar Cardozo's penalty, the Londoners won it when Branislav Ivanovic headed home in injury time.
Artur was despondent afterwards but felt the club were now closer to ending their 51-year wait for a European trophy.
He told reporters: "We did everything we could to win and I cannot explain how we lost because everything we needed to do, we did.
"This is a squad with a lot of quality.
"We made this stage of the competition in deserved fashion and we showed to the world what Benfica are about. We showed that Benfica are now ready to start winning.
"We brought the Benfica fans to another European final after a wait of 23 years.
"This is the rebirth of a sensation that the club hasn't experienced for a while and we will continue to work in the knowledge that good things will happen soon."
Artur accepted a failure to take chances proved decisive, as it did when the sides met in last season's Champions League quarter-final which Chelsea won 3-1 on aggregate.
He added: "We were expecting Chelsea to hit us on the counter-attack but we had total control, we were better, playing some beautiful football.
"We had chances but unfortunately, like last season against them, the cagey but clinical team came out on top."