The Blues scored through Axel Disasi, Christopher Nkunku, Noni Madueke, Cole Palmer and Jadon Sancho as a depleted home team failed to stop the league's top goalscorers.
Enzo Maresca's side could have scored more. Joe Lumley produced important saves, Ryan Manning cleared off the line and Chelsea stuck the woodwork on three occasions.
Southampton's defensive task was made more difficult after club captain Jack Stephens saw a straight red card for pulling Marc Cucurella's hair in the box.
Chelsea registered 26 shots in total and recorded 5.29 expected goals, the highest of any away team in the Premier League since records began.
Speaking at St Mary's, Bree tried to pick out the positives following Southampton's heaviest defeat of the season.
He said: "It was a strange game, obviously, we conceded five goals. That's a problem. It's a weird one because I want to come here and say at times we played some really good football.
"(At times) we cut through them and caused some problems but I think when they got the third goal, and we were down to 10 men, I think it was always going to be an uphill battle.
"We tried hanging in there and making a game of it. If we put away a couple of the chances we had, maybe it could have been a different game.
"I think 5-1 at the end of the day probably flatters them a little bit."
"It's yet another self-inflicted wound!"
Chelsea pounce on Southampton's sloppiness at the back and regain the lead! 🔵#PLonPrime #SOUCHE pic.twitter.com/oNpFiK1cuy
— Amazon Prime Video Sport (@primevideosport) December 4, 2024
Chelsea's second goal came after Joe Lumley passed to an under-pressure Kyle Walker-Peters, who lost the ball, allowing Nkunku to shoot into an empty net.
Asked about handing the opposition another goal, Bree responded: "I think it's so tough because we can create chances from playing out from the back.
"At times tonight, we showed that really well. Obviously, with little mistakes like that, I can understand why it's frustrating for the fans if it keeps happening.
"It has happened a couple of times this season but I think it's just something we've got to persevere with.
"If we can pick the right times to play and if we can eradicate those mistakes and do it right every time then that would be unreal."
Bree played down the idea that Southampton's players will be discouraged from playing out from the back following repeated errors.
"It's tough to take when they do score and capitalise off it, but then look at the nine other times that we've played out and done really well," he explained.
"There's going to be mistakes when you're playing out like that. Sometimes we get lucky and they don't score but it feels like at the minute, if we make a mistake they are (going to score.)
"We'll keep our heads down we'll keep doing it because I think we're getting better and better at it every week. I think we're causing teams problems."