Javier Mascherano turned in Charlie Mulgrew's free kick to give the Scottish champions a shock lead at Camp Nou, only for Andres Iniesta and Jordi Alba to score at the end of each half to break the hearts of the traveling side.
It could have been worse for Celtic, though, with the visitors' defense repeatedly thwarting Barcelona's probing attacking threat.
"We defended with our lives all game," Wilson told Sky Sports. "We thought we had done it [secured a draw], but it is never over until the final whistle against Barcelona, and they proved it.
"Any team that comes [to Camp Nou] don’t get many chances or possession, so that wasn’t a surprise. I think we matched them. It is more of a concentration game against these type of players. One minute [Lionel Messi] is walking, the next minute he spins and he is in [on goal]. You need to concentrate for 90 minutes."
Fraser Forster was Celtic's standout performer on the night, pulling off a string of saves to deny the Spanish giants as they became increasingly frantic in the second half. When asked his opinion on whether he rated Forster - who recently earned his first England call-up - as a world-class player, Wilson was unequivocal in his reponse.
"In my eyes, yes [Forster is world class]. He showed it again tonight. Joe Hart is amazing, but Fraser is up there," Wilson said.
Celtic remained second in Group G thanks to Spartak Moscow's 2-1 win over Benfica earlier in the day and is one point ahead of the third-placed Russians.
Barcelona need just a point to guarantee progression to the next stage, but Wilson believes his team is capable of holding out for the full 90 minutes in the return game.
"Why not? We are at home and our fans love European nights," Wilson said.