"But we have to stay in the hunt, we have to try to keep winning.
This moves us forwards and we'll go from week to week."
Even without the injured David Silva, City began strongly and thought they should have had a penalty when Jose Fonte fouled Sergio Aguero in the area.
But referee Mike Jones booked Aguero, believing he had dived and it took City until six minutes into the second half to break the deadlock.
Aguero laid the ball back to Toure on the edge of the area and the midfielder slammed it into the net.
Southampton were given a lifeline when Mangala was sent off 16 minutes from time for a second yellow card.
But if anything, City were even more dangerous with 10 men as Lampard fired home from the edge of the area to make it 2-0 on 80 minutes.
A City breakaway led to a superb third with full back Clichy the surprise scorer, netting his first goal for the club.
"It's a nice feeling (to score), but the performance from the team was unbelievable," Clichy said.
"I think we controlled the game."
One concern for City manager Manuel Pellegrini was an injury to his captain Vincent Kompany that led to his side ending the game with just nine men.
In the morning's other game, Roberto Soldado scored his first Premier League goal in almost 10 hours to give Tottenham a 2-1 victory over Everton.
After 593 minutes without a league goal, the struggling striker netted his first goal in first-half stoppage time, after Christian Eriksen had already canceled out Everton midfielder Kevin Mirallas' well-struck opener.
By ending Everton's five-game unbeaten run in the league, Tottenham climbed above the visitors from 10th to 7th - just two points from the top four.
-AAP
