In-form Kelechi Iheanacho admits Leicester are out to end the lingering pain of last season.
The striker scored his 14th goal in his last 14 games when he bagged the winner in Monday's 2-1 victory over Crystal Palace.
Three wins from the Foxes' final five games would guarantee a top-four finish – even if West Ham win their remaining matches.
Third-placed Leicester dropped out of the Premier League's top four on the final day of last season and Iheanacho admits it has been playing on the player's minds.
"What happened last season was in our head this season," he said. "We don't want to make these mistakes again. That's why we concentrated to get the win.
"So, these are the type of games we need to win and get the points so that it will help us at the last games.
"We've got five more now, so we need to concentrate on the next and see if we can get the three points.
"It's another big game (against Southampton). We played them in the FA Cup, and they were really strong and aggressive. We've got another chance to play them on Friday.
"We need to come out strong and see if we can get the three points. They're a good side but we need to make sure that we get the three points because we need to be strong."
Iheanacho struck with 10 minutes left after Timothy Castagne levelled following Wilfried Zaha's first-half opener.
"It's a massive three points for us," Iheanacho told LCFC TV. "It's a great night and it was a great finish – I enjoyed that one.
"It's just one thing – I wasn't thinking about anything, just shift and shoot and it could go anywhere.
"It was great character from us. We stayed in the game. It was a sloppy goal at half-time, so in the second half, we changed a few things."
Eberechi Eze set up Zaha for Palace's 12th-minute opener and the mid-table Eagles made the Foxes sweat before a second-half comeback.
Only Jonny Evans' last-ditch tackle stopped Christian Benteke restoring their lead after Castagne's leveller and Eze revealed Palace's frustrations.
"It's a difficult one," he told the club's official site. "I think the boys worked hard.
"We put in a good performance but again, if you make mistakes and you let them get chances, they are eventually going to get chances because they're a good side.
"We've been working hard in training and preparing for this game for a while after the Chelsea game, so we were in a good position beforehand, but we are disappointed."
