Rafael Benitez's men kept pace with early leaders Roma in the opening weeks of the 2013-14 campaign, but fell away in the second half of the season, eventually finishing seven points behind Roma and 24 behind champions Juventus.
Albiol joined from Real Madrid in the close-season, and featured in 32 of Napoli's 38 league matches to help his side to third place and the qualifying round of the UEFA Champions League.
If Napoli are to pose a genuine threat to Juve next season, however, the Spaniard insists they must improve their focus and grind out results.
"The first year in a new team is difficult," he told AS. "There are a lot of changes on a personal level and within the group, but we are pleased with how it has gone.
"As far as slipping up against the lower teams goes, we need to play with more concentration if we want to aim high.
"It's clear that we need to put up more of a challenge in the league. The only thing that makes us different from Juventus is that they managed to win a lot of matches by a one goal margin, while we would often lose points in matches within our reach.
"Napoli will grow, they know how to act in the transfer market and therefore we will grow year by year.
"I'm happy here. It's been a great year for me, I have found consistency and I am pleased."
