Luis Suarez, Raheem Sterling and captain Gerrard's late penalty fired the Anfield outfit to a hard-fought success at St Mary's.
Liverpool remain four points behind leaders Chelsea, who won away at Fulham, but have moved ahead of Arsenal following their defeat by Stoke, and Capital One Cup finalists Manchester City.
Gerrard echoed manager Brendan Rodgers' mantra that the Merseyside club will take one game at a time, but believes their absence from European competition this season could count in their favour.
He told Sky Sports: "I see Theo Walcott's in the studio - they (Arsenal) lost today and we've won.
"I'm sure there are plenty of people around the Premier League looking out for us because we've got no Europe and we're fresh for every game.
"All we asked for at the beginning of the season was to be in it with 10 games to go, and we're certainly in it.
"Chelsea and Man City are still the favourites, but we just have to keep going and try and win every game and with world-class players in the team like Suarez, you can beat anyone.
"It's important to stay calm and take each game as it comes. We haven't got the experience, but we have got a lot of good things going for us.
"The challenge now is can we go and put in a good performance away at Old Trafford and see where we are with four or five games to go. If we're still in it, then why not?"
Gerrard believes Rodgers' tactical switch to a 4-4-2 formation with a midfield diamond to counteract Southampton's pressing game was a key aspect of their victory.
He added: "We dropped points here last year and we learned our lessons. I think the credit has got to go to the manager. He keeps giving us the credit but he had his tactics spot on.
"Our idea was to play a bit longer, try and beat their press and leave two up top. If teams want to play two v two against Sturridge and Suarez - all the best.
"We got it wrong here last year and we maybe got it wrong at the beginning of the season when they beat us at Anfield.
"The sign of a good side is when you learn from your mistakes. The manager changes and tweaks things and we went with a diamond today.
"I thought we were solid defensively and always a threat on the counter."