Disgruntled home fans vented their displeasure following Saints' sixth successive Premier League defeat, with the full-time jeers followed by chants of "you don't know what you're doing".
A precious three points for Forest lifted them out of the relegation zone, while Southampton remain bottom on the back of a fourth top-flight loss since the appointment of Jones.
"I can't pre-empt what fans are going to do," the Welshman said of the boos. "That's entirely up to them.
"It doesn't concern me. It surprises me a little but that's their prerogative.
"The thing about being a football manager, especially when you've come from where I've come from and getting an opportunity here, I understand scepticism and so on. Fans have paid their money, they do whatever they what.
"For me as a manager, you have to be thick-skinned.
"It's not the first time that I've been booed, it's not the first time I've taken stick.
"You have to show real characteristics that bring you through this because when when we come through it, it will be proud moments for me."
Calamitous defending once again contributed heavily to Southampton's downfall as their precarious position became slightly more perilous.
Taiwo Awoniyi fired Forest's 27th-minute winner - the game's only attempt on target - following a sloppy error from Saints defender Lyanco to earn the visitors a first top-flight away success of the season.
Brennan Johnson assisted the goal having earlier struck the crossbar, while Che Adams wasted the best opportunity for the hosts, who slipped four points from safety due to their poor goal difference.
Former Luton manager Jones said Southampton must produce positive results to bring aggrieved supporters back on side.
"That's the only way to change it," he said.
"It was a front-footed performance tonight. We worked hard, we just didn't show enough quality.
"You had a side out there that grafted, that had more situations than Forest and we just didn't show enough quality and then gifted them a goal.
"There's lots we can do better and we have to."
Resurgent Forest have now taken 11 points from the last 21 available, having only managed six from the previous 33.
The two-time European champions were more than comfortable in protecting their slender lead and jubilantly celebrated a first top-flight away win since a 2-1 success at Blackburn in May 1999.
With the match also bringing a first away goal since August, Forest boss Steve Cooper said a fruitful trip to St Mary's ticked "loads of boxes".
"It's better to be out of it than in it, of course, and we've spent enough weeks in there," he said of moving out of the bottom three.
"Now we're out of there, the obvious challenge is stay out of it and, if you can, climb away from it.
"But that's going to be one step at a time, it's much easier for me to say than to do, the same for the players.
"But today's a start, it's our first away win, a goal away from home, which we needed, loads of boxes ticked today in terms of challenges to the players that we managed to overcome and we're good for it.
"The dressing room is really together, particularly the lads who didn't play, which is what I love, what we need.
"I never thought we would concede. I know it's an easy thing to say now but we were comfortable in the game."