Chelsea managed a 1-1 draw against City at the Etihad on Saturday afternoon with Sterling scoring the opener for the visitors before Rodri fired in the equaliser late in the day.
It is the second time this season that Sterling has scored against his old club after grabbing one in the 4-4 draw earlier this season at Stamford Bridge.
But it was the first time that the England international had scored at the Etihad since leaving City in 2022 - though he did not celebrate against his old club as a mark of respect.
However, before kick-off, Pochettino was keen to see the forward enjoy himself if he got on the scoresheet.
When asked about Sterling and another ex-City star Cole Palmer potentially scoring at the Etihad, the Chelsea boss said earlier this week: "When you score, it's the most beautiful feeling.
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"It's hard to keep that in your body and not celebrate when you play for a different team.
"You showed respect when you were there, you gave everything to the club, the badge and the people.
"But when you defend another badge, you need to celebrate because you are part of another history."
Sterling finished off a brilliant counter-attack to put Chelsea a goal up against City just before half-time.
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Some fine work from Nicolas Jackson saw him sprint toward goal as Sterling darted into the box before the Senegal international found him with a cross.
The 29-year-old then chopped inside to leave Kyle Walker on the deck before tucking past Ederson.
However, Chelsea ended up rueing a host of missed chances, with Sterling and Jackson guilty of not putting the Blues further ahead.
Having kept Pep Guardiola's side at bay for most of the contest, City ramped it up late in the day with Rodri grabbing an equaliser on 83 minutes.
While City might have saved a point, it has seen them trail behind Arsenal and Liverpool, who both racked up big wins against Burnley and Brentford respectively.
City are third in the Premier League, four points behind league leaders Liverpool and two behind second-placed Arsenal.
Chelsea, meanwhile, are 10th but are six points behind sixth-placed Manchester United.