Aguero, 29, surpassed Eric Brook's 79-year-old mark of 177 goals in City colours when his 69th-minute strike helped overcome Serie A leaders Napoli 4-2 and seal their place in the knockout stages of the competition midweek.
Pep Guardiola's Premier League pacesetters did it the hard way at Stadio San Paolo, having fallen behind to Lorenzo Insigne's first-half opener.
But further goals from Nicolas Otamendi, John Stones, Aguero and Raheem Sterling capped a dream night for the club's pint-sized scoring sensation.
"I am very happy for this moment. I am happy because the team helped to support me - as did the fans and all the staff. I want to say thank you very much to everyone," Aguero told BT Sport .
"I am enjoying this moment. I am very happy because this moment is a one-time thing."
With the record behind him, and his club in top form, the Argentine expects City to keep on track for the forseable future.
"We will just keep going in the same way," he said. "Every game we play in the same way. It's a long season so now we are in a good place and we must continue in the same way."
In addition to securing their progression to the Round of 16, City's triumph in Italy put them in pole position to qualify as Group F winners.
"Napoli are a good team. Playing away in the Champions League is always difficult," Aguero said.
"I am very happy to win and qualify."