Gerrard scored England's opening goal in the tournament during yesterday's 1-1 draw with the United States, slotting home a perfectly weighted pass from Emile Heskey. But the 30-year-old also showed his worth in making several vital tackles and interceptions when dropping back.
Carragher, who replaced the injured Ledley King at half-time, said: "It's a great achievement to captain your country at the World Cup and I thought Stevie was outstanding. That was not just because of the goal but because he was snapping into tackles as well.
"Sometimes people say Stevie and Frank Lampard can't play in that role -- but Stevie can play the holding role as well as anyone in the world. He can play right back, off the front man, central midfield, attack. At times that's a problem for us because he can play so well in so many different positions. He leads by example and that's what he did against USA."
Carragher feels England will benefit from having played at altitude in terms of their fitness for the rest of the tournament. He said: "We will look at the game, look at the video, look at the statistics and different things. But, at the end of the season and at the end of a match like that, everyone's going to feel it and that's both teams.
"Maybe it [adjusting to the altitude] will improve as we go on. It is always the same at the World Cup. As you go on, you adjust more to the conditions. You don't look 100 per cent in the first game."
Carragher admitted he had to pull out of a tackle on USA striker Jozy Altidore when he burst through on goal for fear of being sent off after having already been booked. It needed a fine save from Robert Green to deny the player who spent last season on loan at Hull and partially atoned for his goal-costing error in the first half.
Carragher said: "It was good play by him [Altidore] but I probably got a bit too tight to him. I had been booked early on so I couldn't afford to make the tackle because I was worried about being sent off. But credit to Rob Green he made a great save that shows the mental strength and character of the man after what happened with the goal."
Carragher also admits he expects to learn a lot from England coach Fabio Capello during the next month after being coaxed out of international retirement by the Italian. He said: "It's a learning curve for me. I might be 32 now but you never stop learning. He has been one of top managers over last 15-20 years so over the next four or five weeks I'm sure I will learn a lot from him. It is a similar way of working to Rafa [Benitez] really, so I'm used to that and I think the players want that sort of intensity."