A Steven Gerrard penalty handed Liverpool the first leg of the Carling Cup semi-final against Manchester City.
"This club should be winning trophies," Adam said. "We are in a semi-final and have an FA Cup game against Manchester United, too.
"The clean sheet against City will give us confidence and we know it will be rocking for the second leg with our fans.
"It will be one of those magic nights at Anfield and hopefully they can get us to the final."
Liverpool have not won silverware since 2006.