The Hammers had led at Upton Park through Mark Noble's deflected effort, but France midfielder Morgan Schneiderlin scored twice before Graziano Pelle's maiden Premier League goal rounded off a fine away day for Saints.
A penalty shoot-out defeat to Sheffield United in midweek saw the Hammers knocked out of the Capital One Cup at their first hurdle and Allardyce's side were not at the races once again.
"We weren't good enough," Allardyce said.
"Southampton taught us a lesson, we weren't sharp enough and didn't retain the ball as well as they did, close down as well as they did and gifted them two goals.
"As much as they were in control and on top of the game, we've lost two very stupid goals from set-pieces."
One bright point for West Ham was the pre-match announcement that they have signed Barcelona midfielder Alex Song on loan.
The former Arsenal man will spend the remainder of the campaign at Upton Park and Allardyce wants to see the Cameroon international "kick a few backsides".
"I hope he can bring a bit of leadership as well as his quality play," Allardyce said.
"The lads are not opening their mouth enough. They all talk about what they should do before the game in the dressing room and in training, but when they go out on the pitch they don't talk to each other. It is clear that their communication is zero.
"Somebody has got to get a grip and open their mouth. If it is a short corner get someone out there. It is not difficult for someone to look around and organise the team. It doesn't appear that anyone is analysing what the situation is and not have the desperate defending that we had.
"Having spoken to him he looks a leader to me and will kick a few backsides on the field. If they are not playing as well as they should do he will get them motivated."