Manager Steve Bruce says Hull's Premier League game against Leicester is "bigger" than the FA Cup final.
Leicester, meanwhile, are five points adrift at the bottom of the table.
"If we go nine points clear of them at the halfway stage, it's a big turnaround to be caught," said Bruce.
"It's a bigger game for me than the cup final."
Hull's win at the Stadium of Light saw them end a five-and-a-half-hour goal drought and climb out of the bottom three.
But they have not won successive Premier League matches since beating Newcastle and West Ham in September 2013 and have taken just one point from the past 12 available at home.
Bruce said: "As we've seen, it's been difficult enough to win one or two games, let alone turn around a three-game swing.
"I could have told you the bottom eight going into January - I might not have got it the right way around, but we have to accept that we are going to be one of them."