Ianni, who was assistant to Sarri at Napoli before joining him at Stamford Bridge this year, raced up the touchline and celebrated with a fist pump right in front of Mourinho.
"It was a good game from Huddersfield and not so good game from us", Klopp told BT Sport.
That may be interpreted as implied criticism of Mourinho, but Sarri was not about to emulate his predecessor, Antonio Conte, in igniting a public feud with the former Porto, Chelsea, Inter Milan and Real Madrid boss.
"No, I'm not annoyed with anything", he said.
"Sarri said he would solve the problem with his assistant internally and he then came to me and apologised and I said if he really meant it then okay, I accept".
"But I have made many mistakes in football matches, especially when I was younger, and I will make many more so when he came to apologise I accepted".
His collected demeanour did not hold up for long though, as he held up his three fingers to signify the number of Premier League titles he won in the direction of the home supporters, who were baiting him as he made his way off the pitch.
United had taken a 2-1 lead thanks to two goals from Anthony Martial after trailing at the break.
The reaction from the fans is not up to me.
"The manager told me to help the team win the game and try and get a result".
As Jose Mourinho prepares to face former club Chelsea on Saturday (Sunday NZT), he is admitting for the first time that the perceived "manhunt" against him is starting to take its toll personally.
Jose Mourinho commended Luke Shaw for being courageous and responding "in the best possible way" to the coach's public criticism after he secured a new long-term Manchester United contract. He was for the first time best player in the Premier League with me, so I think the feelings are good. In this type of football, United are better than us.
Chelsea had most possession and looked in control until Martial thumped in the equaliser in the 55th minute against the run of play after Chelsea goalkeeper Kepa Arrizabalaga had kept out a close-range Juan Mata shot.