Though the Anfield outfit lifted the League Cup and reached the FA Cup final, their worst league position in 18 years eventually cost Kenny Dalglish his job - paving the way for Brendan Rodgers to take charge.
And Adam believes the Merseyside club must work hard to earn the luck which will cure their indifferent home form if they are to do themselves justice next time round.
"They say the table doesn't lie but we didn't deserve to finish eighth. If we had had a bit of luck on our side we probably would have finished higher," Adam told the Daily Star.
"But it's done and gone now. We move forward and hopefully we will finish better than we did last season.
"I can't believe the amount of times we drew at home. It was incredible but you have got to change your own luck.
"If we work hard and do the right things next season we will be further up the table.
"This is one of the best clubs in the world and the opportunity to play here is a dream for any player.
"We have the right people on board and the right players. Hopefully we can keep progressing as a club. Bridging that gap doesn't happen overnight.
"But if you have the right balance, the right group of players and you work hard, you never know what can happen."
Liverpool went on to finish 17 points short of the top four last term, and Adam conceded that the Reds lacked the consistency needed to truly trouble the league leaders.
"Manchester City and United were up there last time because they were consistent the whole season," he added.
"We were inconsistent. We drew too many games."
The 26-year-old also targeted helping Liverpool return to the Champions League whilst expressing his belief that the Europa League will be taken seriously next term.
"Everyone wants to play in the Champions League. It's the pinnacle," he continued.
"For us, we're in the Europa League. We want to try and get into the group stages and try and win every game.
"That's the expectation of this club. It's the expectation of the supporters and the players inside the dressing room."