Blues took a 20th minute lead at Craven Cottage when Seb Larsson scored after being put in on goal following a brilliant run from Alexander Hleb.
However, the hosts earned a 1-1 draw when Clint Dempsey equalised with a headed goal eight minutes into the second half, albeit from a corner that McLeish was adamant should never have been awarded.
"We started slowly in the second half and they undone us," the Blues boss told Sky Sports after the match.
"But in saying that, I think the pictures will tell us that it shouldn't have been a corner.
"How the assistant can give that from the far side, with Ben Foster covering his line of vision, is unbelievable.
"Goals change games and it gave Fulham a big bit of a lift and the fans then got behind them."
The Blues boss was, however, delighted with the contribution that Hleb had in creating Blues' goal: "He showed the blistering pace, that change of pace that we haven't seen," he added.
"We've been working hard on the training ground to get Hleb working at his top level that we've seen him do at Arsenal.
"It was a brilliant goal, it was fantastic play by Hleb. I thought he was gearing up to curl into the top corner.
"But he's found Seb [Larsson], who made a brilliant run, and he's then finished it well because it's not easy to finish from a sweeping move like that.
"But you just hope the supporting player can do it justice, and Larsson did just that."