Nigel Adkins rued a 15-minute period that saw Everton fight back from one-down to see off Saints in a fiercely contested game at Goodison Park.
The visitors were looking comfortable with 20 minutes gone after Gastón Ramírez's first goal for the Club gave them an early lead.
But Leon Osman's 25th-minute leveller and two Nikica Jelavic strikes in the space of six minutes put the Toffees firmly in control going into the break.
The second period was relatively even, with a big chance falling Ramírez's way midway through the half when he chipped Tim Howard before watching his effort sneak agonisingly wide of the far post.
And First Team Manager Adkins was left disappointed his team's attacking approach did not yield the points they hoped to gain, especially after such a bright opening.
"If you look at the way we started in the first 25 minutes, I thought we were very good," he told Saints Player.
"I thought we could get at Everton a little bit and we wanted to be on the front foot away from home.
"We didn't just want to sit back so we've gone with a bit of a diamond formation to try and exploit that.
"It was a good goal from Gastón Ramírez but, after 25 minutes they have gone and scored, so the Goodison roar went up and Everton got themselves on the front foot.
"For that 15-minute spell before half time it is fair to say that it was hard to contain them," admitted the gaffer.
"The second goal was from a counter-attacking play where we had good possession of the ball, and the third was from a cross. I'll analyse them tonight and tomorrow, and we'll probably think we could have done better with them.
"I thought we passed the ball about well in the second half – there was a composure about ourselves to do that.
"If Gastón Ramírez's ball had just rolled inside the post rather than outside, then at 3-2 who knows what could have happened?
"We passed the ball about, played between the lines and put some lovely little diagonals in but unfortunately that little bit of quality evaded us at times today.
"Goodison Park and Everton is a hard place to come to. We didn't stay in the game sufficiently and conceded the goals, so we've got to make sure analyse that and keep everyone strong as positive."
Saints were without Morgan Schneiderlin and Danny Fox, both of whom had started all five of their previous games in the Barclays Premier League.
Adkins revealed: "Morgan picked up a knee injury last week in the last couple of minutes of the game (the 4-1 win over Aston Villa).
"We wanted to keep it quiet and catch Everton by surprise a little bit because Morgan has been outstanding for us.
"All being well, it's not going to be as bad as Jack Cork's [knee injury, which is set to keep him out for the next few weeks] but he'll be touch-and-go for the Fulham game next Sunday. We'll just have to wait and see on that one.
"Danny Fox has had a sore chest all week – obviously I took him off last week and we've looked at the situation where Nathaniel Clyne did ever-so-well last week, as did Frazer Richardson in the right-back position."