Roy Hodgson's side secured their place in next summer's finals by defeating Poland 2-0 at Wembley on Tuesday night, ensuring a fifth consecutive appearance at the competition since they failed to reach USA 1994.
England were knocked out at the last-16 stage by Germany in 2010 but Carragher - a member of Fabio Capello's squad in South Africa four years ago - thinks his country could go one round further this time.
"I think England will have had a good tournament if they get to the quarter-finals," said the Sky Sports pundit, who entered the fray as a substitute against USA in the last World Cup before starting against Algeria.
"It looks like we are going to be involved in a group with top nations and that would make it difficult to get out of, while you also need to take into account that it will be played in South America.
"There are different weather conditions as well, so if England could get to the knock-out stage they will have done well."
Carragher played under Hodgson during the 66-year-old's brief stint in charge of Liverpool, which came to an end after just six months with the Reds sitting 12th in the Premier League.
However, the Croydon-born coach guided Switzerland to the last 16 of the 1994 World Cup and into Euro '96, and Carragher says he is pleased his former boss will get to manage in another major tournament.
"[Roy's] had a long managerial career, so every job is not going to go great," added the Anfield legend.
"The Liverpool one didn't go well, but he then went to West Brom and did a great job and before it at Fulham he did a great job.
"The England job and the Liverpool job are sort of similar because they are high profile, but England is a lot bigger really because the whole nation is looking at you.
"I'm pleased for the country and the players that are there - and for myself as a fan to watch it over the summer - but I am extra pleased for Roy."