A Marcus Barnes double and an Olufela Olomola penalty saw the Magpies surrender their five-match unbeaten run in the Premier League Cup tie on the south coast.
But the scoreline was somewhat harsh on United, who enjoyed plenty of possession, created a number of chances and saw a penalty claim waved away in the second half.
And Beardsley rued his team's profligacy in front of goal, as they tasted defeat for the first time since October.
"They've had a good run, they've played really well and deserve a lot of credit for what they've done," he told nufc.co.uk. "People who weren't there today and haven't seen it would probably say Newcastle got battered today, and that would be a bit harsh.
"But at 2-0 you're chasing the game, and then when it gets to 3-0 it's game over and you've got to try and do what you believe in - to pass the ball, move the ball and keep playing. We had some good situations, but we didn't really look like scoring and fair play to Southampton - they defended well.
"We had plenty of the ball, and even before they scored their first goal, we were probably the better team.
"But it's one of those situations where if you do get a chance, you have to take it. We didn't really look like doing that today."
The Magpies now face Morpeth Town in a Northumberland Senior Cup tie on Wednesday night.
And Beardsley believes that tie at Craik Park is now of greater significance to his side as they bid to bounce back quickly, after their excellent run of recent form was halted by the Saints.
"Sometimes that happens in football. We certainly didn't deserve to lose 3-0, but it is what it is. It's disappointing, but we've got to move on," he said. "We've got Morpeth on Wednesday, which always was a big game but it's even bigger now. They beat us fair and square last time, so we look forward to that on Wednesday.
"They did do very well against us last time and beat us, so we would like to beat them and they'd like to do the same to us this time around. It'll be a physical game, but if we can stand up to that, then hopefully we'll be OK."
