The days of competing in the Champions League, never mind adding to their tally of five European titles, still appear a long way off for Liverpool, but Enrique takes heart from past glories and future promise.
Their standing on the continent could take another hit should they fail to progress into the last 32 in their final Europa League Group A game against Udinese in the Stadio Fruili on Thursday.
It would be only the third time in 11 attempts the Reds have failed to progress to the knockout stages of a European competition.
But Enrique believes Liverpool have to prevail if they are to start working their way back to Europe's elite club competition.
"To be honest, Liverpool before were like Barcelona is now," he said.
"They were the best team and won five Champions Leagues - which is not easy.
"Of course we are not at that level now and it is impossible to compare but this is where we want to be.
"But we have the right manager, the right players and with money to spend from the owners I hope we can be there as quickly as we can and be able to compete for these kind of titles."
A draw could be enough to see Liverpool through tomorrow should it match Young Boys' result at home to Anzhi but defeat would send Liverpool out regardless of what the Swiss team do.
Critics would suggest a European exit would enhance their chances of domestic success but Enrique does not see it that way.
"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 added
"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."