The Ammies, who needed a victory to keep their hopes of a top-seven finish alive, secured a dream start when Jordan Turnbull opened the scoring inside 90 seconds.
However, the visiting Stags – promotion contenders themselves – completed a rapid turnaround through a Stephen McLaughlin double in the first half.
Matty Lund handed the hosts a lifeline when he headed accurately into the corner, but Salford’s efforts were ultimately fruitless.
“The lads are absolutely gutted because they gave everything this season like they have done today,” commented boss Bowyer.
“They’re a great set of lads to work with and we’ve got to come back stronger now. You look at the way that we are on the pitch and we’re going the right way, but we need to get better.
“We started the game ever so well, but I’m disappointed with the manner of the two goals that we concede. It became a bit of a basketball game where we had to go for it, but it was that little bit of craft and guile in the final third which we missed.
“I didn’t think it was refereed particularly well, especially with the manner of the two decisions that led to their two goals. It wasn’t a difficult game to referee, but he wanted to blow his whistle quite a bit. But the way we went about it, we were terrific.”
Mansfield, who could have gone third with victory ahead of the season’s finale, responded well to their early setback.
McLaughlin capped a frenetic opening 15 minutes with a precise free-kick into the far corner and completed the Stags’ turnaround from the penalty spot before half-time.
After Lund’s leveller, the visitors threatened through a lively Rhys Oates but could not find a winner.
Boss Nigel Clough said: “Both teams had to go for it, but I’m unbelievably disappointed with the goals we’ve conceded today. Two headers from the middle of our goal, unchallenged, and that’s what’s cost us the game.
“We’ve had enough chances to win 3-2 or 4-2, especially at the end. They’d got to win and had to go for it, so they were leaving spaces, but our front four didn’t exploit it. We just needed somebody to produce a little bit of quality today to win the game.
“We got into some great positions and (Nathan) Bishop didn’t have too much to do. I’m just disappointed after that really good 20 minutes that we played that we didn’t really get back onto it.
“It feels like an opportunity missed today because the goals that we conceded were really poor.”
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