Sadio Mane scored 13 Premier League goals for Liverpool last season after joining from SouthamptonSadio Mane scored 13 Premier League goals for Liverpool last season after joining from Southampton (AFP Photo/Glyn KIRK)
A 34 million pounds ($44.5 million, 40.1 million euros) capture from Southampton, Mane struck a 15th-minute opener and then supplied the cross from which ex-Liverpool player Javier Mascherano scored an own goal.
"I'm happy with the result and with a lot of the game," said Klopp, who lost James Milner to a first-half heel injury.
"I don't want to over-estimate this game, but it's still good for us. We didn't think that we were lower than Barcelona before the game and we don't think that we're higher than them after the game."
Liverpool play Mainz, one of Klopp's former clubs, in a friendly in Germany on Sunday before tackling Arsenal in their Premier League opener next weekend.
Barcelona's defeat meant that Paris Saint-Germain won the International Champions Cup friendly tournament for the second year running.
Barcelona coach Luis Enrique was missing Neymar, who is on duty with hosts Brazil at the Olympics, but fielded both former Liverpool striker Luis Suarez and Lionel Messi, who hit the post in the first half.
Barca play Sampdoria at the Camp Nou in their final pre-season friendly on Wednesday and face Sevilla in the first leg of the Spanish Super Cup on August 14.
"From the beginning we saw two teams with completely different rhythms," said Luis Enrique.
"It was definitely not our best day. But there's enough days for us to prepare and there's no doubt we'll be competitive."
- Milner injury -
The glamour game drew 89,845 spectators to Wembley -- the stadium's second-highest attendance -- and it was Liverpool's fans, comfortably in the majority, who went home with smiles on their faces.
With seven friendly matches behind them to Barcelona's two, Liverpool were the sharper team and they took the lead with a slick goal.
After winning possession on halfway, Adam Lallana surged forward and exchanged passes with Roberto Firmino before teeing up Mane, whose rising shot beat goalkeeper Marc-Andre ter Stegen.
Liverpool had to weather a succession of Barcelona chances before half-time.
Suarez, facing his former club for the first time, teed up Messi to roll a shot against the right-hand post, while Liverpool goalkeeper Simon Mignolet saved from Arda Turan and Suarez.
Milner, who announced his England retirement on Friday, was again deployed at left-back for Liverpool, but had to give way to Alberto Moreno before half-time. Klopp said he would undergo a scan on Sunday.
Within three minutes of kick-off in the second half, the game was as good as over.
In the 47th minute, Origi's flick released Mane and his low cross from the right was bundled into the net by Mascherano.
Barely a minute later, Kevin Stewart caught Jeremy Mathieu dawdling on the ball and freed fellow half-time substitute Origi, who coolly beat Barcelona replacement goalkeeper Claudio Bravo.
Grujic, signed from Red Star Belgrade in January, put the cherry on the cake in added time, meeting fellow Serbian Lazar Markovic's scooped pass with a fine header that looped over Bravo.