The Hammers were handed a £5.5million fine for breaking transfer regulations last week regarding the signings of Carlos Tevez and Javier Mascherano.
The Upton Park outfit feared they could have been docked points for the offence, but they managed to avoid such a punishment.
Collins admitted it was a relief to all the players and he is now confident they can win their battle to avoid the drop.
"It was hanging above our heads for all the time we have been down there," Collins told the Daily Star.
"To have it cleared up and have no points deduction is a big boost.
"Now we have to worry about keeping West Ham in the Premiership.
"I believe we can stay up. We are full of confidence, and results breed that.
"We have had a good team spirit all season."
