The Premier League's two surprise packages go head to head on the south coast having made light of pre-seasons predictions that both could be involved in the relegation scrap.
Southampton remain third in the table with 14 games remaining - a position they retained after West Ham shared a 1-1 draw with Manchester United at Upton Park on Sunday.
Sam Allardyce's men were agonisingly close to a famous triumph, only for Daley Blind to cancel out Cheikhou Kouyate's superb opening goal with an injury-time equaliser.
It left a bitter taste at the end of a stirring West Ham performance, but Cresswell insists there will be no issues with his team-mates feeling sorry for themselves as they remain in European contention.
"We got one point instead of three, but we're still full of confidence," the former Ipswich Town full-back told West Ham's official website.
"We deserved the three points over the 90 minutes, but it wasn't to be.
"We've been there before over the Christmas period when you play Saturday/Tuesday or Saturday/Wednesday. We'll be full of confidence going to Southampton on Wednesday and we're all looking forward to it.
"Obviously we've had a good first half to the season, you could say. We're well into the second half to the season now and we're eighth in the league."
Southampton head into the match having chalked up their 11th league clean sheet of the season in Saturday's last-gasp 1-0 win at managerless QPR.
The Southampton defence has only been breached on 17 occasions - the fewest number of goals conceded in the Premier League - and it is a record that goalkeeper Fraser Forster is justifiably pleased with.
"As a team we are proud. We defend from the front, work very hard out of possession and put teams under pressure," the England international told BBC Radio Solent.
"It's credit to the team, and the back four have been so important in limiting teams' opportunities against us.
"If you can keep it 0-0 as long as possible, with the quality we've got up front, we're always going to score goals."
Southampton's well-organised backline will once again be without Ryan Bertrand (suspension) and Toby Alderweireld (hamstring).
Matt Targett deputised for Bertrand at QPR, but is doubtful after suffering a first-half head injury, even though manager Ronald Koeman confirmed the youngster had escaped serious damage.
Midfielder Kouyate operated as an emergency centre-back amid his goalscoring heroics at the weekend and Allardyce will hope to be able to bolster his defence with Winston Reid and James Collins, who missed out against Manchester United due to hamstring injuries.
Striker Andy Carroll will have his ankle problem assessed.
