Mauricio Pochettino’s Spurs were rocked by stunning goals from Philippe Coutinho, Ivan Rakitic and two from the irrepressible Messi.
Harry Kane, and then Erik Lamela, briefly gave the hosts a chance of taking something from the match by cutting the deficit to one goal.
But Messi’s second in the last minute put paid to that, meaning the late collapse at Inter Milan now looks even more costly for Tottenham who have no points from their opening two matches in Group B.
Pochettino praised his players for making Barcelona fight for their victory after the visitors’ fast start.
“I want to congratulate the team because we were always in the game. It was massive in the second half, we were fighting and never gave up,” he said.
“What can you say? What can you do more? I think it’s impossible. I’m so proud. I’m disappointed with the result but the effort was massive.”
He added: “Of course there were a few mistakes, that is clear.”
That was in reference to a question about the costly charge off his line from Lloris, and Pochettino said goals conceded can often be the outcome “when you make a mistake at this level”.
The Tottenham boss said he was “disappointed for that”. And he also had praise for Messi, his fellow Argentinian, saying: “He’s a fantastic player and not because I tell you but the most important is because Messi in every game shows why he’s Messi.
“His average performance I think is this type of game, that is always above everything.”
Liverpool received a taste of their own medicine as Napoli scored a 90th-minute winner to inflict a 1-0 defeat on Jurgen Klopp’s side in the Stadio San Paolo.
Two weeks ago the Reds snatched a winner of their own deep into added time to beat Paris St Germain but the tables were turned in Naples with Lorenzo Insigne sliding home from close range 30 seconds from the end of normal time. In truth the hosts, who also hit the crossbar through substitute Dries Mertens, deserved it having dominated against a Liverpool side putting in one of their worst performances under Klopp.
Klopp said: “We had our moments. It was an interesting group before we started and it’s still interesting.”