The only goal of the game was scored in the first minute of stoppage time when Ian Henderson, a player who City looked at in the summer, latched onto Jordan Turnbull's pass to chip the ball over Sam Hornby as the hosts appealed for an offside flag in vain.
Replays seemed to show that the Salford forward was in an offside position and Ammies chief Gary Bowyer making his first return to BD8 after his sacking in February, 2020, admitted it was a decision that could easily have gone against his side.
But it was Salford's night. Two points behind City at the start of April, they are now ten points in front and moved into the play-off zone on Tuesday night.
Trueman said: "Watching it back, it looks offside and the linesman makes an easy decision to keep his flag down. With the manner we lost it, we are disappointed.
"In terms of a reaction, we had it and our performance levels were probably better than they have been in a while, but that probably says where our performance levels were before. But it is a tough one to take for us, the staff and the players.
"There was one just before (a decision) he does not give and then he does not give us a big decision and that is their job."
Trueman and Sellars threw down the gauntlet to the players ahead of the game and took several to treat the final matches as akin to a job interview in an attempt to ensure that they are in the duo's plans next season.
It came following criticism in Saturday's loss at Port Vale when players' character and fight was questioned.
Trueman continued: "I asked for us to be a bit more competitive and improve our performance levels and we did that. We started bright and for long periods of the game, we were on top and Chas (Charles Vernam) had a good chance early on and Cooky (Andy Cook).
"We came in at half-time knowing we just needed to keep focused and keep creating those chances to finish them to give ourselves the best opportunity of winning the game. We knew the next goal would be vital.
"We spoke at half-time about if we did not finish those good chances we created and we looked to create in the second half.
"The Cookie (Callum Cooke) one was pulled across and we should never had put ourselves in a position where we could lose the game late on. That is the biggest learning curve for us."