The Reds sit two points off Premier League leaders Arsenal in second place after 11 games, as they aim to finish in the top four for the first time since the 2008-09 campaign.
|13/2||Liverpool are 13/2 with Coral to win the Premier League this season|
"A good start was something we targeted and prepared for," he told the Liverpool Echo.
"But the season is very long and we just go from game to game trying to get as many points as possible.
"All of us believe that this season we can stay towards the top positions and get back into Europe. To play in the Champions League is the dream for every player.
"We are working hard every single day to achieve that. I hope at the end of the season we will be happy."
Skrtel had been linked with a move away from Anfield this summer but ultimately stayed, and he says he is happy with his decision.
"I have been here at Liverpool for six years and it's been a great six years for me," he continued.
"Playing for such an illustrious club like Liverpool for six years is something any footballer would be proud of.
"I will be 29 in December, I have a contract here for three more years and I am very happy. I will keep striving to do my best and see what that time brings.
"Now I am just trying hard to keep myself in the team, and that's not easy with six centre-backs competing for two or three places."