The 23-year-old was playing his first match since November 4 after recovering from shoulder surgery.
"Our players couldn't have done any more. Some of our interchanging and creativity was outstanding," Rodgers said. "Sometimes you have days where the keeper makes one or two good saves, but we had 14 shots on target away from home today.
"I know Alex well. He's genuinely going to be a top, top keeper and to perform like that having been out for so long was absolutely staggering."
Rodgers worked with McCarthy during his six-month spell as Reading manager in 2009 and tipped the academy product for England honours.
"Reading has always produced very good goalkeepers so he was down the pecking order at the time," he said. "He has all the qualities to be a top, top keeper - he's 6'5", makes good saves, is good on his feet and is very calm and assured despite being very young.
"Absolutely I can see him playing for England, there's no question about that.
"It will be hard because Joe Hart is one of the top five keepers in world football, so it will be very difficult for him because Joe is still very young.