The result means that seven points now separate City from fifth place, and Guardiola acknowledged that it is another step towards their goal of qualifying for the Champions League.
"Congratulations to the team, especially the way we played. We were able finally to make 15, 20, 25 passes in a row. Up front we could be better but our quality of play meant we had control. This result is so important for our qualification for the Champions League," he told BBC Sport.
"Every manager Vincent Kompany has played under knows what an important player he is. Finally, in recent games he has played he has delivered performances and hopefully he can stay fit. I want him fit enough to play every week - he has suffered for a long periods but he is a real, real central defender.
"In the first half we controlled the game but Southampton were good out wide. But after we scored they had to press us and so we were able to find our passes between the lines much easier. And with players like Kompany and Silva we have players who can deliver on the counter-attack."
City will drop back down to fourth place in the table should Liverpool avoid defeat at West Bromwich Albion tomorrow.