The supposedly friendly match threatened to boil over at times in sweltering Shanghai, particularly during a bad-tempered first half.
There was a flashpoint between the Premier League rivals when United accused Moussa Sissoko of stamping on winger Daniel James.
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Spurs' attacking midfielder Dele Alli was earlier booked for two nasty challenges and booed off when subbed on the hour.
Team-mate Japhet Tanganga and United's Andreas Pereira were also yellow-carded.
"It's true that I was a little bit annoyed about some situations and not happy -- it's a friendly," said Pochettino.
"When you are tired and hot, sometimes you are not right and arrive late (to tackle). I apologise on behalf of our players to United."
But the Argentine, who took Spurs to the final of the Champions League last season, said that Ole Gunnar Solskjaer's side were not blameless themselves.
"In the second half they did the same to us," he said.
"I was worried. When something happens in pre-season (an injury), it's tough."
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His Norwegian counterpart said he thought the International Champions Cup match was a good test for the tough season ahead.
"No tippy-tappy football," he said.
"No qualms about some of the tackles. You are worried (about injury), but no injuries.
"We also gave (it out), we did not just receive."
United made it four wins from as many pre-season games thanks to a winner from teenager Angel Gomes.
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United defender Eric Bailly had to be stretchered off in the second half with what could be a serious knee injury -- there was no suggestion Spurs were to blame.
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