The result sees Barca fail to advance into the last eight of the competition for the first time in 14 years.
Messi’s stunning equaliser had given the visitors hope of staging a remarkable comeback after Kylian Mbappe had earlier put the hosts in front against the run of play with a penalty.
Ronald Koeman’s side had arrived at the Parc des Princes seeking to become the first side to overturn a three-goal deficit from the first leg at home by delivering a performance on the scale of ‘La Remontada’
But some wasteful finishing, including Messi’s penalty that was deflected on to the bar by PSG goalkeeper Keylor Navas on the stroke of half time, sealed their fate.
Replays suggested that Messi and Barca might have had a case for a re-take with PSG midfielder Marco Verratti appearing to encroach before the spot-kick was taken, but VAR ruled against that.
And a day after watching his old nemesis Cristiano Ronaldo bow out of the competition with Juventus, Messi befell the same fate.
Having suffered chastening 7-0 and 8-2 exits to Bayern Munich in recent years and been dismantled by Mauricio Pochettino’s side in the first leg at the Nou Camp, few would have held out hope of a Barcelona comeback prior to kick-off.
But the manner in which they set about PSG from the off was, at times, reminiscent of the Barcelona of old and there could have been few complaints had the Catalans gone some way to retrieving their sizable deficit before half time.
Ousmane Dembele in particular was guilty of spurning several excellent opportunities, while Sergino Dest was unfortunate to see his powerful drive cannon to safety off the crossbar after the faintest of touches by Navas.