Backhouse felt Theo Vassell had committed the foul, but Bowyer disagreed.
“I thought we started very well and took the game to a team that had won eight of their last nine games,” said Bowyer.
“We scored a very good goal from a set piece and had another great opportunity.
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“I thought for 30-35 minutes we controlled the game and we made them change their shape.
“But the game changed on a free kick when Theo Vassell was clearly fouled and the referee gave it the other way.
“That said, once it's been given against us we have to defend it and it was an appalling goal to concede.
“To compound that we then go and concede another. They should not be able to score from there if we line the wall up proper.”
Bowyer was impressed by home striker Rhys Oates, who netted the equaliser.
“You look at their centre forward today – he never stopped running and putting defenders under pressure,” he said.
“I felt towards the end of that first half we stopped putting them under pressure up top.
“We have not been played off the park. Second half we've camped in their half but we've just not had enough quality in the final third to unlock them.
“Credit to Mansfield. They run hard, they've got energy all over the pitch, they close down and they make it difficult for you.”
The defeat left Stags 11th and Salford 17th but Bowyer said: “There is nothing in this league. I know people will go – look where you are in the table.
“Mansfield have just won nine out of 10 after not winning for 14 games. That shows you this league. There is nothing to be scared of.
“That was our first league defeat in five and we need to regroup and go again.”