With Monday night's Premier League match delicately poised, Liverpool's hopes of coming away with victory were dented when Spearing, starting in place of the injured Lucas Leiva, was handed a straight red card by referee Kevin Friend.
Friend deemed that Spearing's challenge on Moussa Dembele was worthy of a sending off, after the midfielder took the ball but also caught the Belgium international on the ankle.
Fulham's Clint Dempsey went on to score the winner, and Dalglish was left to rue the defeat, in particular after seeing his rivals for a top four finish all claim victories at the weekend.
"He won the ball," the Scot told Sky Sports 1. "He probably upset the referee with his follow-through but it's not his fault there's somebody standing there.
"You see them sometimes get a red card, other times they get away with it. The problem everybody has is the level of interpretation - that's not consistent.
"I think we would have taken something if we'd been left with 11 men. I don't think we played as well as we have been but we did enough to come away with something but we haven't done it."
Fulham boss Martin Jol, however, felt the red card was justified. He said: "I think it was a bad tackle. His ankle was there and I think it was a sending-off."
Jol also reserved praise for match-winner Dempsey, who capitalised on a mistake from goalkeeper Pepe Reina to pounce for the decisive goal with five minutes remaining.
The Dutch coach said: "Clint is a good player. He scored 13 goals in the league last year and tonight it was a much-needed goal and a much-needed win.
"We dropped points at home against Everton when we were the better team - we were pretty unlucky. Tonight we had the rub of the green. We weren't the better team but it was even.
"Mark Schwarzer is one of the best in the business and he saved us."