Both goals came in the second half, Jermaine Beckford putting Bolton ahead before Alex Baptiste's own goal saw Wednesday equalise.
Two controversial decisions then came with Johnson's disallowed goal for offside and then Semedo's reckless challenge seeing them down to 10 men with five minutes left.
Jones was not happy and stated he would appeal Semedo's red card.
"It wasn't a sending-off," he said. "They had a youngster who should have been sent off and it should have been a goal.
"Hopefully, Chris (Foy) will review it and see that the lineslady was very quick in lifting her flag and I can't see where the offside is.
"As for the red card, you can normally tell by the reaction of players and that's what Semmy is all about and that's not his game.
"That's why he was so upset. His foot has slid across the floor and he's taken the ball. I just feel that some of the big decisions weren't right and we'll certainly be appealing."
Jones was pleased with his side's performance, though, and added: "I can't fault my players' efforts at all because they were fantastic throughout and we're doing everything right.
"Chris Kirkland has pulled off two terrific saves at the end but up until the sending-off there was only one winner for me."
Bolton manager Dougie Freedman believes the referee had a good game and said his side were unlucky not to take all three points.
Wanderers remained searching for their first home victory and slipped back down to 21st in the Sky Bet Championship table - just two places above their winless opponents.
But Freedman was content with his team's display and insisted it was just a matter of time before the Trotters triumphed at the Reebok Stadium.
"We started very well and we were playing some fantastic stuff and Jermaine scored a beautiful goal, but once again at home there was a huge piece of misfortune for us with the own goal," he said.
"I thought that we coped very well at the back and probably won the battle in the air at the end against a very good Sheffield Wednesday front four.
"We are playing very well at the minute and we showed great courage to get in their and try and force a winner and we had four or five really good chances to do that in the end."
On the red card and the disallowed goal, Freedman added: "As soon as anybody leaves the ground then you run the risk of being sent off.
"I've seen the video and he's jumped off the floor and committed a dangerous tackle on Jay Spearing.
"For the goal the guy's a yard offside and the assistant referee's done very well to spot it, to be fair."