Uruguay and Liverpool striker Suarez is expected to recover from a knee injury in time to face England in Thursday’s crunch match in Sao Paulo.
He has been castigated for racist comments and biting other players in the past, but this year Suarez has enjoyed a season free of controversy and full of goals.
Suarez scored 27 times this year to bring Liverpool within a whisker of ending their 24-year wait for the league title.
There was many a stunning effort in that haul, but for Hodgson, a player has only proven himself when he lights up a World Cup.
When asked whether Suarez belonged in the same “world-class” bracket as Lionel Messi and Cristiano Ronaldo, the England manager said: “I think he will only be at that level when he shows it on this particular stage.
“He has got the potential. He is he a wonderful footballer. But if you are really going to put him up there with [Diego] Maradona, Pele, [Franz] Beckenbauer and [Johan] Cruyff, and [Andrea] Pirlo, this is the stage you have got to do it on really.
“You can be a great player in your league but for the world to recognise you are one of the all-time greats you have got to do it at the World Cup.”
Hodgson may live to regret those comments. Suarez loves nothing more than proving his critics wrong, and after Saturday’s shock defeat to Costa Rica — in which he was an unused substitute — his country needs him more than ever.
England’s own talisman, Wayne Rooney, needs to have a good tournament to prove he is worthy of being bracketed as one of the best in the world too. After nine World Cup appearances, Rooney’s goal tally still stands at zero.
In Manaus he worked tirelessly as usual and set up Daniel Sturridge for his goal, but he blew two good chances to find the net himself.
“We want him in the area more,” Hodgson said. “I thought he set up the goal really well with that clever pass.
“Then after Leighton Baines put him in with that pass I was convinced he was going to score when he got himself room in the box.”
England had Italy on the ropes in the opening 15 minutes, but they could not beat stand-in goalkeeper Salvatore Sirigu until just before half-time, when Rooney picked out Daniel Sturridge to score.
“We have got to ally the pace with scoring goals,” Hodgson said. “We have got to be a bit more ruthless.”
Despite Italy winning the game with goals from Claudio Marchisio and Mario Balotelli, Hodgson is far from downbeat about England’s chances of progression and thinks his team has enough pace and venom to see off Uruguay and Costa Rica.
“We won’t panic,” Hodgson said. “It was as positive performance as I have seen from us. And it gives me great hope going forward, not just the next two games, but further than that.”
ENGLAND: Hart, Johnson, Cahill, Jagielka, Baines, Gerrard, Henderson (Wilshere 73), Sterling, Rooney, Welbeck (Barkley 61), Sturridge (Lallana 79).
ITALY: Sirigu, Darmian, Paletta, Barzagli, Chiellini, Verratti (Thiago Motta 57), Pirlo, De Rossi, Candreva (Parolo 79), Balotelli (Immobile 73), Marchisio.
Ref: Bjorn Kuipers (Netherlands).