Saints looked in control at 2-0 up at half-time against the team they beat in the Premier League on Saturday, but the Potters fought back and levelled through Mame Biram Diouf with eight minutes remaining.
Stoke appeared to be the more likely winners at that stage but Peter Crouch saw red for two yellow cards in less than a minute.
The second was for a foul on Steven Davis and, from the resulting free-kick, an error by Erik Pieters allowed Pelle to grab his second in the 88th minute.
Koeman said: “We played well. It was more difficult when they made it 1-2 after half-time.
“In the first half we scored two great goals and were much the better team on the pitch. They showed more character after half-time, real fight, but we created three big chances for the third and didn’t take them.
“They were physical and brought Crouch in, and it’s difficult to defend. It’s not the way I like to play but that’s Stoke.
“Maybe after the red card for Crouch we were a little lucky but we deserved to win, we had more chances than Stoke.”
Pelle has been a key figure in Southampton’s run of nine wins in 10 games and took his tally for the season into double figures.
“Pelle is a great player and showed his qualities, not only scoring, but as a target man,” said Koeman. “Little by little the players are learning how to play with Pelle. He’s been a great signing for us.
“You can’t always win the football way. Stoke made it very difficult and made it a battle in second half. But my team showed spirit. Even after the disappointment of going to 2-2, the feeling was positive on the bench.
“I had the possibility to change players and I was confident if it went to extra time.”
Southampton, who have never won the League Cup, will travel to Sheffield United in the last eight.