Pellegrini praised Michail Antonio and matchwinner Sebastien Haller, who combined dangerously together to threaten the Saints throughout as the Chilean switched to a 4-4-2 formation at St Mary's.
The manager said: "Both of them worked very well attacking. We knew Southampton were a team who concede goals and both of them had different actions, one inside the box, and the other running into space. We had a few more chances too. Antonio is an important player as is so many of the players we are missing. We know he makes an impact. He can improve more and I think we will see him score more. Both of them played a complete game both defending and attacking.
"I think they did very well, both of them, and we scored one goal but had two or three more clear chances to score.
"Michail demonstrates every time he plays that he's an important player. You must add Manuel Lanzini, Jack Wilshere, Lukasz Fabianski. They are all important players, but we know Antonio makes an impact because of his power. Unfortunately for him he had the handball [which saw his goal disallowed seven minutes after half-time], but we played a complete game attacking and defending."