The win was comfortable enough in the end but Stanley caused plenty of problems for their visitors in the opening 45 minutes and were unlucky not to be ahead at half-time.
The League Two outfit attacked from the first whistle and having fallen behind to Nevland's strike against the run of play, they took only four minutes to equalise through top-scorer Michael Symes' 14th goal of the season.
The sending-off of Reds defender Darran Kempson shortly before half-time changed the game, but Hodgson believes that up to that point, only the commanding performances of centre-backs Brede Hangeland and Aaron Hughes had kept Fulham in the match.
"You don't play against that many teams that never stop the ball at the back but just hoist it forward into your back line again," Hodgson said.
"I was happy that we have got two big centre-backs in that situation who can head the ball.
"Otherwise we could have been in even more difficulties."
An uneven playing surface also made life difficult for Fulham and Hodgson admitted the conditions his players have grown accustomed to in the Barclays Premier League meant they would inevitably struggle to adapt at first.
"You get very spoiled in the Premier League," Hodgson said.
"You can talk about these pitches and you can talk about these conditions, but until you actually get out there and experience them, it's only words.
"You need the actual physical experience on it because we're so unbelievably spoiled these days in the Premier League.
"Every pitch you play on is like a billiard table and it's so much easier to pass the ball."
Having been in the ascendancy with 11 men, Accrington faded after Kempson's dismissal and could offer little once Duff had put Fulham 2-1 up on the hour.
Stanley boss John Coleman's immediate reaction to the goal was to go for broke by bringing on-loan striker Billy Kee off the bench.
The visitors' dominance only grew though, with Gera netting the third 10 minutes from time.
Coleman, who is in his 11th year with Stanley, admitted afterwards that he had been too bold in the heat of the moment and vowed to learn from the experience.
Coleman said: "Maybe I put an extra forward on too quickly to try to get back in it. I have got to take the responsibility for that.
"I am learning and maybe next time it happens to me and I am up against a Premier League team with 10 men, I will take it on the chin for a bit and see if we can nick a goal elsewhere."
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