The former Manchester United fullback announced his retirement this week.
Carragher, who played alongside the Manchester United star for England, told talkSPORT: "For me he's the best full-back the Premier League's had. And also just behind David Beckham probably one of the best crossers of the ball we've seen.
"People always talk about the rivalry between Liverpool and Man United and of course it exists. We want to beat them and they want to beat us but I have great respect for Man United as a club and I hope that's vice versa.
"Were two of the most successful teams, two of the biggest teams in the world, and for me Gary Neville's been one of the main reasons why that's happened.
"A great player, great pro and to play at that level for so long is a fantastic achievement so I take my hat off to him."