The Three Lions skipper believes his side can cope without the Manchester United striker in the first two group games, as Hodgson's men prepare for the opener against France
The Manchester United striker was handed a three-match ban by Uefa, since reduced to two, following a kick-out at Miodrag Dzudovic in the 2-2 draw against Montenegro in October 2011.
But the 32-year-old midfielder thinks the Three Lions are more than capable of putting in good performances until Rooney's return.
Gerrard told RMC: "Wayne [Rooney] is a world class player. Any team would suffer after the loss of such a player.
"So yes, we will miss him. But we hope it will go well without him and we can do the job. In any case, we expect to reach the quarter-finals."
The Liverpool man also praised the quality of the France squad ahead of the two sides' meeting in their opening group game on June 11.
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He continued: "Playing against France for the first game is a difficult start because this team is fantastic. But this type of game is exciting.
"They are fantastic players. For example, we know Nasri and Benzema very well. When we see such players selected for France, we understand that the quality of the French team is high.
"I consider France to be one of the favorites for the Euros. We are all looking forward to playing this game."
However, Gerrard refused to look past the match against Les Bleus, insisting that his side will take it step by step.
"We take the games one after another," he added.
"Sincerely, we hope to first achieve a good result against France. What we do will automatically give a lot of confidence for the rest."