The recent season included only six home wins at Anfield and an eight-game suspension of Uruguayan striker Luis Suarez for repeatedly calling a Manchester United player a racially insensitive slur. There was also speculation that a lack of African players on the roster has hurt Liverpool.
Asked if the lack of racial diversity has hurt Liverpool, Rush said, "No I don't think so. I think it's just their home performances. Liverpool can beat any team in the world on a day. They beat Manchester United, Manchester City.
"What they have to do is learn to beat the so-called lesser teams. What happens is that teams come to Liverpool, they're game as well. Whether they're playing Manchester United or Manchester City or Swansea, they have to go into the game with the same attitude."
Rush believes that Manchester City's championship this season is good for the league despite some who think the team bought its way to a championship similar to the way that the Red Sox finally won the World Series in 2004.
"You cannot buy history," Rush said. "What Manchester City will find out over the next few years is that they're in the same league as Manchester United and Liverpool were. Teams will be game against them next season. Everyone wants to beat them."
Werner, the team chairman, said that Rodgers will change the style of Liverpool.
"In Brendan we have acquired a very exciting and talented and young manager," Werner said. "He's a forward-thinking coach at the forefront of a generation of young managers and will bring to Liverpool attacking, relentless football."