Chelsea are seven points behind rival Tottenham Hotspur for fourth, who have a game in hand on them.
Southampton pushed for an equaliser in the closing stages, but they were unable to carve out another chances as Chelsea held on for the win.
Super Eagles winger Victor Moses was a very late substitute with just four minutes action as Chelsea survived initial scare to win 2-3 away to Southampton on Saturday.
'The players must play like this [in the second half against Southampton] in every game, not for me, but for the club, ' said Conte. This is the best possible way for a player to show that he is a fantastic professional.More news: Lahore HC bans airing anti-judiciary speeches of ex-PM Nawaz Sharif
"Our first half wasn't good in a lot of aspects, not only tactically, but didn't show great spirit desire or the will to fight for a good result".
Christian Eriksen reduced the arrears in fortunate circumstances, his initial shot blocked by Aymeric Laporte before deflecting back off the Dane and past the stranded Ederson, with Sterling adding the third in the second half. Olivier we know very well, we are talking about global players. We have six games in the league.
Chelsea manager Antonio Conte refused to comment on Alonso avoiding any punishment for the tackle, but praised his players for shaking off a woeful first-half showing at St. Mary's.
Antonio Rudiger was omitted from the matchday squad to face Southampton despite being fully fit, and some have suggested that his absence was a response to him appearing to question Chelsea's tactical approach in a TV interview after the West Ham draw.More news: Three Bodies of Missing Indian American Family Found; Little Boy Still Missing
"After 15 minutes I said we'd be champions, after what happened and we reacted", said Guardiola, who will be on the golf course with his son when United play on Sunday.
'It was tough for us, the second goal was a hard moment but the most important thing if you concede one or two goals is to never give up and believe in our quality and play our game. The most important thing is this. I'm the first person to take my responsibility.
Had he opted to remain with Arsene Wenger's side, the 31-year-old's first-team opportunities would have, in all probability, been further limited following the arrival of Pierre-Emerick Aubameyang from Borussia Dortmund during the January transfer window.More news: United Kingdom government pledges £61m to fight plastic waste in Commonwealth countries