Despite easing past Debreceni 1-0 in Budapest last night, the Reds were eliminated from the competition after Fiorentina beat Lyon by the same score in Florence.
It means Liverpool will now play Europa League football for the first time since 2004 in the New Year and has given the club's critics even more ammunition.
Mascherano, though, believes Rafa Benitez's squad have a duty to the club's supporters to put the setback behind them as quickly as possible and treat the Europa League in the same way they would the Champions League.
The Argentine midfielder has even set his sights on go all the way to the final, which will be held in Hamburg next May, to make up for missing out on a trip to Madrid.
'It's a strange feeling for everyone at the club,' said the Argentine midfielder. 'The Champions League is a special competition for us but it's gone and we must keep going.
'Now we are in another competition and we will do all we can to win that. There will be no problem with motivation. The motivation is simply to play for Liverpool.