Brendan Rodgers' side were top of the Premier League on Christmas Day, but now sit fifth in the table after consecutive 2-1 defeats at Manchester City and Chelsea.
Liverpool have not competed in the Champions League since 2009-10, but have established themselves as one of the leading contenders to finish in the Premier League's top four this season.
The Merseysiders' home form was a major factor in their strong first half of the campaign, with them having won eight of their nine top-flight games at Anfield, scoring 25 goals in the process.
And Brazil international Lucas feels continuing this trend in 2014 is key to their hopes of reaching Europe's premier club competition for next term - starting with victory over Hull, who beat Liverpool 3-1 in last month's reverse fixture at the KC Stadium.
"If we want to be in the top four, we want to win these kinds of games," he told the club's official website.
"It will be a great opportunity to win, as we lost against them away from home. To get three points is the most important thing and to keep climbing up the table.
"It's becoming a very hard place to come. Probably our record in the last few years at home was not the best, but we're getting back to what Anfield used to be - a very hard place to come and play against us.
"We are happy with the way we are playing the games and beating teams at home. We just hope we keep that going on New Year's Day."
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