The Dutchman celebrated his 52nd birthday by watching his side close the gap on Manchester United and Liverpool in the race for Champions League qualification.
Southampton are now just three points behind United in fourth place after Shane Long and a Jason Shackell own-goal handed the hosts the deserved victory.
“Three points was my best present today,” Koeman said.
“It was a difficult one in the first 45 minutes. They had one or two chances which were unlucky and two great saves from Kelvin Davis but I’m very pleased how we played in the second-half. We were in total control of the game.
“We scored good goals and had other chances to score. I’m very pleased about the second half. It’s all about confidence. The team was looking very comfortable and we looked good in our ball possession. That’s the football I like to play. It’s looking positive.”
Both Southampton strikers, Long and Graziano Pelle, went into the game with a goal drought hanging over them.
Long ended his 14 game blank but Pelle, who hasn’t scored since December, struggled throughout and missed a glorious opportunity in the first half when he hit the crossbar from six yards out.
Koeman was pleased with the way both strikers performed and believes the goals will eventually come for Pelle.
“It’s always important for strikers to score,” he said.
“Shane had been doing an outstanding job in the last few weeks. He’s more comfortable and confident in how we play. He was struggling a bit at the beginning of the season and he’s now playing at a great level.
“That’s football. You can’t change that. The one thing you have to do as a striker is keep working and one day you will score. Pelle had some good chances today but he was unlucky. If he keeps working the goals will come.”