Birmingham City and Reading were both relegated from the Premier League on Sunday despite winning their final matches of the season.
Fulham's 1-0 win at FA Cup finalists Portsmouth, courtesy of Danny Murphy's second-half header, meant they escaped the drop with 36 points.
Reading also finished with 36 after a 4-0 win at relegated Derby County but had an inferior goal difference. Birmingham, who beat Blackburn Rovers 4-1, ended on 35.
"It's a lonely place at the moment the dressing room, the players have got to let it sink, we've got to let it sink in.
Then we will make some cold decisions," Reading manager Steve Coppell told Sky Sports.
"I feel like I've let (the chairman) and the club down to some extent because I don't feel like we should be in this position."
Fulham, promoted to the top flight in 2001, stayed up at Reading's expense after wining four of their last five matches, three of them away having previously gone all season without a win on their travels.
"For all the plaudits we are getting I can also appreciate how the relegated teams are feeling," Fulham manager Roy Hodgson, who took over from Lawrie Sanchez in December, told Sky Sports.
"For long periods of the second half I was contemplating that feeling myself. The last 10 or 15 minutes were the most difficult ... when we actually got the goal my main thought was for God's sake don't let them score."
Birmingham City returned to the Championship after just one season up. "It's over 38 games and we didn't quite make it," Birmingham manager Alex McLeish, who replaced Steve Bruce in November, said. "Congratulations to Fulham."
