The Reds were held to yet another home draw against Stoke last weekend, their seventh at Anfield so far this season.
Those dropped points mean the club have fallen out of the European places and are five points adrift of Chelsea in the final Champions League position.
When quizzed on whether Champions League qualification is still the club's main aim, Adam told Sky Sports News Radio: "Of course it is, it's still there, there's plenty of points to play for, you never know what is going to happen.
"We have been disappointed with the results as well but that's expected, we are a new team gelling, it takes time but we'll do everything we can.
"For us, it's trying to win every game and on the day it's not always happened for us.
"But we'll not stop working hard and keep doing the things that we know is right and trying to win as many matches as we can.
"The most important game is the next game, a difficult game away at Bolton, which we are looking forward to as we have to bounce back after last week."
On a personal level, Adam revealed how quickly he has settled at the club following his big-money move from Blackpool and urged other young Scottish players to try and follow his lead in the English game.
"It's been great," he added. "When you join a new club, sometimes it takes time to settle in but it's been easy for me with the players that we've got here. They have made me welcome and I'm thoroughly enjoying it.
"Since I've walked into the door at this club, I've enjoyed every minute.
"I've always been told to play with a smile on my face as I'm in a very fortunate position where I'm at one of the biggest clubs in the world.
"For our national-team manager, I think he would expect his best players to be playing at the highest level, playing against the best players to improve.
"For me, the Premier League is the best league in the world and it's a top league. Now you see the number of English clubs going to the Scottish market as they know the value for money is there.
"They don't have to pay over the odds for players but they're getting good quality for what they are paying for."
