At the halfway point in the campaign, the Tigers have outperformed their fellow promoted clubs considerably, sitting 10th in the table with Cardiff City and Crystal Palace 16th and 17th respectively.
After rounding off 2013 with a 6-0 mauling of Fulham on Saturday, the Yorkshire club will travel to Liverpool on New Year's Day - a team they beat 3-1 on home soil on December 1.
Hull's first ever Premier League campaign in 2008-09 also saw them get off to a quick start, but they only survived by a point come the end of the season and Koren has warned his colleagues of the perils of complacency.
"We're halfway through the season now and we've got points on the board. It's been a really good start," the Slovenian told the club's official website.
"But this is the Premier League and we know we have to keep up our concentration in every game because we know that three points are available every time we play.
"From past experience, we know that this is a really tough league. You can go three or four games without getting a result and then there are problems.
"Hopefully we can keep going as we are with the good performances and getting points for those."