The Tigers enter the new year 10th in the table and high in confidence after thrashing Fulham 6-0 at the KC Stadium on Saturday.
Koren, who scored twice against Fulham, told the club's website: "We're halfway through the season now and we've got points on the board. It's been a really good start.
"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."
Prior to the weekend Hull had not won in five games, but the only defeats in that sequence were against league leaders Arsenal and champions Manchester United.
They were also impressive in the 3-2 loss to United on Boxing Day, having led 2-0 and also gone close to snatching a late equaliser.
They also have good recent memories of playing Liverpool having beaten Brendan Rodgers' Reds 3-1 just a month ago.
The Fulham game had been former West Brom player Koren's first start since that victory over Liverpool and he is keen to continue in the team and with that winning feeling.
The 33-year-old Slovenian said: "I haven't seen a second-half performance like the one we put in before in my career.
"To score six goals in 45 minutes showed that we have something special in our team.
"It was really good for our confidence and hopefully we can keep going.
"I'm just glad to be here playing football. I started the season well, but then the foot injury took me off track a little bit.
"I do my job every day in training and I'm looking after myself, waiting for the chance to play.
"I started the game on Saturday and scored two goals and I'm really happy about that."
- Sports & Recreation
- Premier League
- Steve Bruce