Landmark goals from Guly do Prado and 18-year-old substitute Sam Gallagher secured a 2-0 win at St Mary's that booked Southampton's place in the fifth round.
Guly converted a penalty midway through the first half to score for the first time since January 2012, while Gallagher's 70th-minute strike represented the young Scot's first senior goal.
Although the Premier League side hit the woodwork twice and ultimately progressed with a degree of comfort, Championship strugglers Yeovil carved out several opportunities inside the first hour.
Perez acknowledged as much afterwards, saying: "It wasn't an easy game. The first half was open. They had some chances to score.
"In the second half, we were much better and created lots of chances."
Perez was also pleased to see Guly and Gallagher on the scoresheet.
Of the Brazilian, he said: "He's been working hard. He deserved his chance and his goal."
Gallagher also came in for praise, with Perez adding: "He's still young and needs time, (but) he's doing well. He scored a nice goal."
