The left-back moved to Upton Park on a six-month loan deal from Manchester City last week and made his Hammers bow against Arsenal.
But Bridge was given the runaround by Theo Walcott and was at fault for every goal as the Gunners won 3-0.
Torrid time: Bridge (right) struggled to cope with Arsenal winger Walcott
'It was a difficult game for me really,' he told the club's official website. 'Theo is really quick and that was my first 90 minutes for a while. I've not played too many this season so I had a bit of cramp at the end but I didn't feel too bad for the first 60.
'I'll just improve next week and things can only get better. I try not to look too far ahead. 'We have got Everton at the weekend and I just want to win. One thing I don't want to see is West Ham go down.'
West Ham are rooted to the foot of the table and play Everton at the weekend before heading for Birmingham with a 2-1 lead in their Carling Cup semi-final.
Bridge added: 'We should just take one game at a time and hopefully we'll end up staying up and getting a medal.
'It's a bonus for me to be allowed to play in the League Cup and it would be lovely to end up with a winner's medal.'
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