The rock-bottom Tigers go into Friday's clash against the Toffees at the KCOM Stadium having won only one of their previous 16 league fixtures and losing their last three in a row.
While Everton will certainly fancy their chances of inflicting another defeat, Koeman has emphasised he was impressed by some of what he saw from Hull in their last two outings, a 1-0 reverse at West Ham and 3-0 home loss to Manchester City.
When it was put to him that Everton fans may well be expecting another victory to add to the 2-0 Boxing Day triumph at Leicester, the Dutchman said: "Yes, but that's the most dangerous thing you can do in football, because we know the Premier League is unpredictable.
"Maybe you expect a win, and then it will be totally different.
"I don't look to the classification, the position in the table, because I watched Hull against Manchester City
After 70 minutes it was still 0-0 and City were not creating a lot of chances.
"Also, Hull lost the game at West Ham 1-0 but they were the better team and hit the post several times.
"So don't focus on positions in the table
It's a tough one, a difficult one and we need to be at our best to get a good result."
Seventh-placed Everton registered their first away win since September with the Boxing Day result, halting a run of four straight defeats on the road.
Koeman has no doubt how important that was for his players ahead of Friday's contest, in which he wants them to go about their work the same way as they did in the second half at Leicester.
"Of course, it's always difficult if you're not winning away or you don't have those kind of performances to be happy - then you need to break it," he said.
"The win (against Leicester) was good - the way we played in the second half, the way we controlled the game (Everton scored both of their goals after the break).
"We need the same attitude on Friday."
Goalkeeper Maarten Stekelenburg will be missing once again on Friday when Koeman's side look to make it three wins from four matches.
Stekelenburg was ruled out of the Leicester game with a dead leg and remains sidelined, with Joel Robles set to continue in his place.
Midfielder James McCarthy (hamstring) is also still unavailable, as is full-back Bryan Oviedo (unspecified), while Yannick Bolasie and Muhamed Besic are both out of action due to long-term knee injuries.
Source : PA
Source: PA