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 Europa League.
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 Premier League clash with Southampton.
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, but 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."
The Magpies, who will have full-back Mathieu Debuchy and striker Yoan Gouffran available after their absence in Kharkiv - they are ineligible to play in the European competition - will head into the game intent on putting right what went wrong in the reverse fixture at the St Mary's Stadium in November.
That day, they turned in an insipid performance to go down 2-0 to goals from Adam Lallana and Gaston Ramirez in a defeat which proved to be the third in a depressing run of nine reverses in 11 league outings, and one which plunged them deep into trouble.
They have rallied since - successive victories over Aston Villa and Chelsea have steadied the ship - but the job is far from complete, and 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 had a scan yesterday and is due to see a specialist on Monday, and 26-year-old Rob Elliot will make his league debut for the club with teenager Jak Alnwick on the bench as Steve Harper battles a knee problem.
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."
However, the manager will hope to have midfielder Cheick Tiote, who was withdrawn from the team an hour before kick-off in Kharkiv because of a virus, and full-back Davide Santon, who did not travel because of an ankle problem, back, while he will be able to recall rested central defender Steven Taylor.
But as the manager drew up his plans, he was able to reflect on the growing strength of his new-look squad after debutant Massadio Haidara shone at left-back and fellow January signing Mapou Yanga-Mbiwa turned in an imperious individual display alongside skipper Fabricio Coloccini in the heart of the defence.
Pardew said: "Massadio, I would have no problem putting him in now after his performance.
"The two guys who were really making their debuts in their positions - Mapou at centre-half and Massadio at left-back - were as good as I could possibly have asked for."