Elliot suffered season-ending knee ligament injury while on international duty with the Republic of Ireland.
Benitez has revealed that the 29-year-old goalkeeper is determined to return to competitive action as soon as possible.
"It was very bad news for us and for Rob, but I saw him the day after and he's quite confident he'll be back as soon as possible,” the Spaniard told The Northern Echo. "He's very positive and I was surprised because it's a bad time for him.
“We can do nothing at the moment, we can't sign another keeper, so we have to wait and support him and hopefully he's back a soon as possible.”
Benitez has also revealed that Karl Darlow will replace Elliot in the Newcastle starting lineup.
"Now we have to concentrate on what we can do, and we have to support Karl all we can,” said the former Liverpool and Chelsea boss. “Mentally he's right to come in, he's confident and we know he can do it.
"From what we've seen in training he's a good keeper with good qualities and he's confident. A team has to defend from the strikers backwards and we'll try to protect Karl like we would any keeper."
Darlow, who is 25 years of age, is set to start for Newcastle against Norwich City away from home at Carrow Road in the Premier League on Saturday afternoon.
The former Nottingham Forest man is a good and talented goalkeeper, but he does not have much Premier League experience.
The Englishman has played just once in the English top flight, but from Benitez’s comments, it seems that he is ready for the challenge.
Newcastle are second from bottom in the Premier League table at the moment with 25 points from 30 matches.
The Magpies are in real danger of getting relegated to the Championship at the end of the season.