A draw against Udinese at the Stadio Friuli on Thursday night 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 Barclays 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 told Press Association Sport.
"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.
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