Despite going into the second leg with three goals advantage, the Argentine and his Catalan teammates were unable to save their qualification with just one goal.
As two goals each from Divock Origi and Georginio Wijnaldum helped Liverpool achieved one of the greatest comebacks in the history of the championship and qualify with 4-3 on aggregate.
Before yesterday's fixture, the 31-year-old had netted 12 times in 10 UCL appearances this campaign, but failed to add to his tally at the end of the match.
Similar occurrence happened last season when the La Liga giants were bundled out same competition at the quarterfinal stage by Roma after surrendering 4-1 lead after both legs.
Liverpool managed to keep the 31-year-old quiet all game, with The Guardian giving him a rating of just four out of 10.
"No magic this time," they wrote. "Had a second-half sulk as the dream of another final collapsed around him.
"Beaten long before the final whistle. "
However, Messi is said to have failed to find the back of the net beyond the round of 16 away from home since 2013.
After scoring during his side's 2-2 draw against Paris Saint-Germain in the quarter-final according to Give Me Sport quoting Per Squawka.
Meanwhile, Liverpool boss, Jurgen Klopp was able to silence the five time Ballon d'Or winner at Anfield and managed to overturn the 3-0 result from the first leg.
While Barcelona's solution could very well be new additions in the summer, as a deal has already been agreed with Ajax for midfielder Frenkie de Jong, while his teammate Matthijs de Ligt may follow in the summer.
Given Suarez's return in Europe, it wouldn't be a surprise to see Barcelona splash the cash on a new striker as well. Anything to help Messi out.