Malcolm Clarke, chair of the FSA, has urged rail chiefs and the football authorities to ensure supporters due to travel to away games this weekend do not lose out as a result of the decision to suspend the programme as a mark of respect.
Clarke told the Press Association news agency: "There's a big question there about refunds, advance train tickets that have been booked for away games and all of that.
"We would certainly expect the rail industry and the football authorities to take a very sympathetic view of that.
"It's not a good time to ask fans to spend money on things that don't happen."
The Football Association, of which the Queen was a long-standing patron, announced on Friday that all fixtures scheduled for this weekend from Premier League and EFL level down to the grassroots game would be postponed.
Other sports, most notably cricket, golf and both rugby codes, opted to go ahead as planned with tributes being paid beforehand.
The FSA said in a statement on Friday: "We believe football is at its finest when bringing people together at times of huge national significance - be those moments of joy or moments of mourning.
"Our view, which we shared with the football authorities, is that most supporters would have liked to go to games this weekend and pay their respects to the Queen alongside their fellow fans."
Competitors, officials and spectators as the BMW PGA Championship at Wentworth, the third Test between England and South Africa at the Oval and the Betfred Super League play-off eliminator between Huddersfield and Salford were able to do just that.
Asked if that reinforced the FSA's view, Clarke, who admitted there was a range of views even within its membership, said: "We feel that there were other ways of paying tribute that would have actually been more meaningful than simply calling everything off, particularly with things like kids' football.
"I'm sure that the youngsters could have found better ways of doing it than sitting at home on their Xboxes or going out with their parents to alternative events."