Victory at Upton Park would also see the Saints make it six wins on the road in the Barclays Premier League season, an historic achievement for the club.
West Ham are also in fine fettle and are riding a three-match winning run in the league while they have kept a clean sheet in their last four matches, including a goalless result against Chelsea.
"West ham has improved a lot in recent games," Pochettino said. "They are doing a great job defensively.
"We know we are going to have a tough game.
"We need to increase our level in order to win."
Southampton are 11 points clear of West Ham, who are 11th in the standings, four points clear of the drop zone.
However, Pochettino knows his side is in for a difficult afternoon.
"They are strong and hard to play against," he said. "They have good players.
"They know what it is to fight in these situations.
"This is a time in the competition where every game is a battle and it's hard.
"Every match from now on demands a lot of effort both physically and mentally."
Last weekend's 1-0 defeat at Sunderland knocked the Saints out of the FA Cup and halted their seven-match unbeaten run in all competitions.
"We have a lot of respect for every competition," Pochettino said. "We had a bad night and we didn't hand a good performance.
"I can understand the fans' disappointment.
"We all feel the same frustration as we wanted to win and progress to the quarter-finals.
"Against Sunderland, we put out a team that was fresh and that we thought could get the job done.
"We didn't progress because we didn't play our best as a team not because of the team selection.
"The one thing that saddens me is that in saying certain things, one lacks respect for those players that went out and played on Saturday.
"All my players are capable of playing in the Premier League and playing for Southampton.
"They are all professional."
Southampton are unbeaten in the league since falling 2-0 at home to Chelsea on January 1.
They are eighth in the standings with 39 points and on course to defend their top-flight status for a second straight season.
"We are fighting to defend our position in the standings," Pochettino said. "It's important for Southampton to finish as high as possible in the league, it would be a big achievement.
"The Premier League is one of the strongest competitions in the world and it's not the same to finish seventh than eighth or ninth."
The Argentinian tactician, who is in his second season at the club, believes this is an important year for the Saints.
"We are consolidating a project, a philosophy and a style of play," Pochettino said. "We have young players that need to gain experience.
"We have many aims to look forward to but we have to grow as a team.
"We have a lot of young English talents that are not only going to be important for Southampton but for England in the future."