Saints fell behind to a Sergio Aguero goal inside the opening 10 minutes at St Mary's before hitting back thanks to Dani Osvaldo's sublime curling effort.
Both sides pushed for a winner but it was Southampton who enjoyed the majority of possession and Pochettino was proud of the spirit they showed, even with a number of key players sidelined due to injury.
"We are fully aware that there are going to be periods during the season when we have more or less injuries. Now we are having a period when we are having a lot of injuries, and we stood up to that well today," Pochettino told Sky Sports.
"We have shown the right mentality today by playing as a team and getting a positive result."
Asked if Southampton had a tactical advantage with an extra man in the centre of midfield, Pochettino said: "I don't think it is about the system, it is more about the energy.
"We actually had more possession than Manchester City, against the team that has the most possession in the Premier League.
"Overall today we are happy with and proud of the point we have got, but I think overall we deserved more.
"We could have got a win today. We weren't able to do that, but I think my team played very well."
Pochettino was also thrilled that Osvaldo, who joined Southampton from Roma in the summer, made such an important contribution by scoring the equaliser.
"There is no doubt it is going to be a massive boost for his confidence," said the manager.
"We have always said that the adaptation to this league takes time, but I think today he showed that he can do amazingly well, that he has great talent and that his adaptation is coming along just fine."