Sean Dyche's men opened their Premier League campaign with a spirited display against the title favourites, with Arfield's sensational strike firing Burnley ahead in the 14th minute.
Goals from Diego Costa, Andre Schurrle and Branislav Ivanovic in the remainder of the first half gave Chelsea a lead they would not surrender but Burnley will take plenty of encouragement from their efforts.
And Arfield said the squad were not disappointed and simply even more determined to record their first top-flight points since 2010 when they visit Swansea City on Saturday.
"Obviously to play against a top-quality team like that we knew it would be a tough game," Arfield told the club's official website.
"I thought we did OK... Chelsea showed their quality and their rotation in the middle of the park in particular was different class.
"It was there [for all] to see what top players they are and what a top team they are.
"We got an early goal but even after that, we were under no illusions as to how tough it was going to be and there are definitely positives to take out of it.
"For us it is still a case of taking one game at a time and there is no disappointment regardless of this result, we're on to the next game now.
"With the fans behind us anything can happen. I think they'll have gone home happy with what they've seen in the second half and the high pressing game we like to play."
Arfield said his early goal was a special moment and dedicated the strike to his family.
"I was absolutely buzzing [when that went in]. I've waited a long time to play in the top division and I enjoyed it," he added.
"On a personal level that was different class and my family were down here from Scotland to see it too.
"They've stuck by me and they've waited a long time for that too, so it was a really special moment."
