Warne will miss September's Commonwealth Games and the following tour to Pakistan, and is in doubt for the Ashes series later in the year.
"You never like to lose your key players, but you've got to try and win games when things aren't all going your way, and that's going to be a new challenge for us," Taylor said.
"Warney has been an absolutely outstanding bowler for us for a number of years now. We've got to try and find other ways of getting people out."
McGrath was in outstanding form before succumbing to a stomach injury which reduced him to just one Test last season.
However, Taylor said he was hopeful of McGrath's full recovery in time for the Pakistan tour. "He's very keen to get back into it and, like most competitive sportsmen, doesn't like sitting on the sidelines - and I'm sure he's looking forward to Pakistan."