The Magpies returned from Ukraine triumphant during the early hours of Friday morning after the previous night's 1-0 win over Metalist Kharkiv had secured their passage to the last 16 of the competition.
But Gutierrez insists their clash with Southampton is far more important to their season.
The two clubs are locked together on 27 points in 15th and 16th places respectively with the Saints better off in terms of goal difference.
Both are only four points clear of the drop zone and that is a situation Newcastle are determined to remedy this weekend.
Gutierrez said: "That's the most important thing, the most important thing for us is the Premier League.
"The Europa League is a really nice competition, but if you don't do it right in the Premier League, you find yourselves fighting against relegation.
"We don't want that, so we have to be focussed on the next game in the Premier League, that's the most important thing for us.
"All the sides in the Premier League are really tough, the games are really difficult.
"Southampton have changed their manager and they have got a few points from the last games, so it is going to be really difficult.
"We are confident, but we know they are a good team as well. We believe in ourselves, but we can't be over-confident and think it is going to be easy because it's not going to be like that."