It was only once Stanley defender Darran Kempson had been sent off just before the break for a challenge on Zoltan Gera that the Premier League side really began to assert themselves.
Second-half strikes from Damien Duff and Gera sealed a 3-1 victory which was comfortable in the end for Fulham, but Hodgson readily acknowledged that his team had been unsettled by Accrington's early endeavour on the bobbly surface.
"I don't think we adapted very well to the conditions in the beginning of the game," Hodgson said.
"A number of balls just ballooned into our final third. Accrington played a lot of football through the midfield and we weren't quite expecting that every ball would be lashed forward.
"So credit to Accrington, they made it very difficult for us to get those balls out.
"They made life very difficult for us but in the second half we showed them more of our qualities and ended up winning the game relatively comfortably.
"All credit to Accrington for the magnificent show they put up."
Despite seeing his side battle well against a team who were 70 places above them in the football league at the start of play, manager John Coleman believed Accrington should have been able to build upon their early superiority.
"I am disappointed with the result and with the three goals we conceded," Coleman said.
"I thought we were the better team until they scored their second goal, but once we went down to 10 men we got a bit disjointed.
"They hadn't been anywhere near our goal until they scored that first goal, and that was disappointing, (coming) from a set play when we had worked on it.
"The second one was from a set play as well and that could have been stopped.
"But we have played them off the park in the first half and it is a bit of a travesty that we only went in (at half-time) level."
The sending-off of Kempson by referee Stuart Attwell was an undoubted turning point in the game, and asked for his reaction to the decision, Coleman said: "I think the referee will have to assess his own performance and he will have people assessing him."
Accrington are currently within touching distance of the play-off positions in League Two and Coleman hopes the confidence his players will take from their performance can give boost their promotion bid.
"We can take heart from that but now it is all about our league campaign," Coleman said.
"We can't get to Wembley in the FA Cup but maybe we can get there via the play-offs."
Source: Team Talk