A draw against Udinese at the Stadio Friuli tonight could be enough to see the Reds advance to the last 32, should it match Young Boys' result at home to Anzhi.
Defeat, however, would send Liverpool out regardless of what the Swiss team do.
And while critics of the competition have suggested Liverpool, currently 11th in the Premier League, could do without the distraction of European football, Enrique disagrees.
"I want to play in the Europa League. It is not a 'funny' competition - it is a privilege and in my opinion everyone wants to play," he said.
"That is why we have brought a strong squad because we want to be in the next stage.
"It is not the Champions League - that is the best thing and there is no comparison - but it is another competition and another title you can win.
"For the players and fans it is another cup to play and, if you have the chance to win, why not try?
"I think the Champions League is where Liverpool have to be but it is in Europe against teams like Udinese. Liverpool have to be there, in Europe."
Manager Brendan Rodgers feels the same and has the bonus of being able to play leading scorer Luis Suarez in his first European away game against the already-eliminated Italian side as he is suspended for Sunday's trip to West Ham.
Only captain Steven Gerrard (illness) and defenders Glen Johnson and Daniel Agger (rested) have been left behind as the Northern Irishman looks to secure their place in the knockout phase.
"To not have Steven Gerrard here certainly weakens you because he is a world-class player, but it is unfortunate because he is ill and it is too much of a risk for him to travel," Rodgers said. "It is just about making sure he is okay for the weekend. "It is important we don't rely on one player and this is about the team and that is what we will rely on (tonight).
"But Luis is a world-class striker and when you have a world-class operator in your team it certainly makes you a better side.
"He would have liked to have played in more of these games but I've been trying to manage the group and give others an opportunity.
"It is a great game for him to showcase all his qualities."