Victory over Brighton and Hove Albion on Monday saw Hull progress to the FA Cup quarter-finals at a time when Steve Bruce's men are 11th in the top-flight table, six points clear of the bottom three.
Koren scored the winner in the 2-1 success over Brighton, only his third goal of the season in all competitions, and has warned that the prospect of two trips to Wembley should not see his team-mates lose focus in the club's attempt to avoid a return to the Championship after promotion last season.
"We have come so far, just one game from Wembley, of course we want to do well," the Hull captain told the club's official website.
"To get to Wembley would be special for each of us and the same from the fans' point of view.
"We must concentrate on one game at a time and make sure we are strong in the league.
"Our main thing this season is to stay in the league and Newcastle is a really important game for us."
Hull face Newcastle United at the KC Stadium this weekend looking to record a first win at home in the league since the 6-0 demolition of Fulham in late December.
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