The Belgian, who joined the Toffees on a season-long loan on transfer deadline day from Chelsea, has scored three times for the club in his first two appearances to help the Merseysiders climb to fourth in the Premier League table.
Lukaku netted a brace and bagged an assist as Everton edged out Newcastle United 3-2 on Monday night, and Carragher feels that his form could help the side finish high up the table.
"He's the type of player you look at as defenders and you think 'that's probably why I retired'. You don't really want to be coming up against players like that," Carragher told Sky Sports News. "He has the goals, the power and the strength, but did you see the pass for the second goal for Barkley and the weight of that pass? He's got so much about him.
"If you think about the Everton sides under David Moyes they were solid defensively and had good compact midfields but they always lacked a standout striker. They had Tim Cahill, who'd play off the front and would get goals, but you look at this lad in his first game-and-a-half in the Premier League for Everton and he's got three goals and one assist. Have they ever had a striker of that quality?
"David Moyes got them to the Champions League once and they got knocked out in the qualifying round and Roberto Martinez says Bill Kenwright put him under a little bit of pressure in his first interview by mentioning the Champions League. But they are there now and with this striker that they haven't had before then who knows?"
Everton travel to Manchester City on Saturday.