While he conceded that failure to take numerous scoring chances cost his side victory after taking the lead, Silva was furious that Palmer's leveller was allowed to stand.
Aleksandar Mitrovic headed the visitors into a 50th-minute lead after Harry Wilson nodded a cross from Neeskens Kebano back across goal.
It looked like being enough until 11 minutes from time when Palmer, introduced as a substitute just three minutes earlier, volleyed home from a narrow angle after Chris Martin's shot was saved.
"The goal was clearly offside," said Silva. "It wasn't a difficult decision and I can't understand why the linesman failed to spot it.
"I have seen a replay, but I knew at the time from the bench that it was offside. A poor decision has gone against us.
"I wasn't happy with our first-half display. But we made a couple of changes at the interval and the second half was much better.
"The substitutes made an impact, but the whole team played with more purpose. We just have to be calmer with our finishing.
"There were so many clear opportunities created, but we couldn't get the second goal to kill them off.
"We have to do better in that respect. We moved the ball well in the second half and could have had the game wrapped up before they scored.
"The game was played in a fantastic atmosphere, which was good for us. I respect Bristol City and in the first half we didn't play the way we wanted to.
"We controlled the second half, although they had some chances as a very good counter-attacking side.
"Unfortunately, we couldn't add to our lead and the linesman has given one goal to them, which never should have been."
Mitrovic squandered three golden chances in the closing moments alone. Twice the striker shot wide when he should have scored, while his third effort clipped the crossbar.
Jean Michael Seri also saw a late effort deflected against the woodwork, but City also created chances and boss Nigel Pearson was encouraged.
He said: "The players showed great tenacity against good opponents. While Fulham could have had more goals, so could we.
"I'm not kidding myself and we have a lot of work still to do, but the players know their jobs and that they have to defend as a team."
Pearson praised the home debut of right-back George Tanner, a summer signing from Carlisle, but was again frustrated by a home record that now reads 15 games without a win.
"That continues to be a concern," he said. "But the players are giving everything to turn home results around and if that continues it will happen.
"I said when we signed George that he was one for the future, but he has come in today and done very well."
Pearson felt Fulham midfielder Nathaniel Chalobah should have received a second yellow card in the first half before being replaced by Silva at the interval.
"He was guilty of two poor challenges after being booked, which were yellow card offences," he said.
"The fact that he was substituted at half-time probably says it all. But I'm more concerned with my own players and again they gave a fully-committed performance.
"I'm not bothered whether our goal was offside or not. That is for their manager to debate.
"It was a tight game in the first half and the second shows that you cannot open up too early against a team including a lot of players with Premier League experience.
"We had to be positive at 1-0 down and that left a few gaps. But we also had chances late on and overall I'm pleased.
"I expect all my players to work hard and that was the case."