Alan Pardew's side travel to Russia this week for the first leg of their last-16 tie with Anzhi Makhachkala.
Gutierrez is adamant that a fight for Premier League survival must remain the Toon's first priority following Saturday's 1-0 defeat to Swansea City.
The Argentine told The Sun: "We have four games in the next two weeks that are going to be really, really tough.
"The Europa League is nice but the Premier League is our priority. I've been in Spain and England and seen big teams playing in the Champions League but who are in the bottom three.
"We need to start taking the points to make ourselves feel comfortable. Ask the fans of Newcastle if they want to win the Europa League and get relegated. I think they will say no. The most important thing for Newcastle is the Premier League."
The Magpies are currently 15th in the table but remain just six points clear of the relegation zone.