“I have heard the ridiculous rumours about me resigning, and I can tell you there is not an iota of truth in any of them,” he said, according to mirror.co.uk.
“The simple truth is that I have never considered resigning, and I never will.”
Hodgson praised Liverpool supporters after they were targeted by Napoli’s hard-core ‘Ultra’ fans in the hours before the goalless Europa League draw.
Six English fans – four of whom suffered knife wounds – and one Italian were hurt in a spree of co-ordinated attacks using a variety of weapons.
Despite a heavy police presence, there were a few other incidents with one group of about 10 Liverpool fans being pelted by missiles on the way to the game.
However, Hodgson hit back at Italian journalists who had asked him what he felt about “drunken Liverpool fans coming to Naples and causing trouble”.
“I was aware and I was concerned about the attacks,” he said.
“These supporters have done a fantastic job; it was always going to be tough asking them to come to Naples as they know they are coming to a potentially dangerous situation.
“All I can say how grateful we are for their support and how sympathetic and sad we were to hear they had been attacked and some of them seriously.
“We don’t want violence on the pitch or off the pitch and we certainly don’t want situations where supporters don’t want to go and support their team because they are frightened of getting injured.
“In the press conference yesterday a question was asked of me in Italian – and I answered in Italian – as to whether I was concerned drunken Liverpool supporters would cause trouble on the streets of Naples.
“I find that now faintly amusing that I should be defending Liverpool supporters from Italian journalists when in fact they are peaceful people who come here to watch the game and some of them end up being stabbed.”
On the pitch a solid display saw his side keep only their second clean sheet in the last seven matches — the other came in Utrecht on their last European outing — and although they have not won in that time there were plenty of positives. The closest Napoli came to scoring was in first-half stoppage time, when Marek Hamsik’s shot was cleared off the line by Paul Konchesky.
Liverpool had a couple of chances of their own late in the second half, with Ryan Babel shooting straight at goalkeeper Morgan de Sanctis while David Ngog saw his shot blocked by Salvatore Aronica.
“There were plenty of positives to come from the game,” added Hodgson.
“It was a good point which many people didn’t think we would get, considering the team selection, but we’ve proved them wrong.
“We are delighted with a point which keeps us top of the table.”
De Sanctis, Campagnaro, Cannavaro, Aronica, Maggio (Zuniga 75), Pazienza, Gargano (Yebda 83), Dossena, Hamsik (Sosa 85), Lavezzi, Cavani.
Reina, Kelly, Carragher (Kyrgiakos 46), Skrtel, Konchesky (Aurelio 65), Jovanovic, Poulsen, Spearing, Babel (Cole 77), Shelvey, Ngog.
Referee: Thorsten Kinh.