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.
However, while fans started to dream of a long-awaited first major trophy since the 1969 Fairs Cup, manager Alan Pardew and his players were focussing only on Sunday's vital league clash with Southampton.
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."
Gutierrez knows compatriot Mauricio Pochettino's side, who beat champions Manchester City last time out, will be no push-over.
He said: "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."
Pardew has lost keeper Tim Krul, potentially for several weeks, after he left the Metalist Stadium on crutches after a robust challenge by striker Jonathan Cristaldo.
The Holland international is due to see a specialist on Monday, and 26-year-old Rob Elliot will make his league debut for the club. Pardew said: "I would have no qualms about playing Rob. He's been absolutely brilliant in training, so I would have no problem with that."