Ralph Hasenhüttl hailed a night he will never forget as his Southampton side hit four goals without reply at Fratton Park in his first south coast derby.
Boyhood Saints fan Danny Ings scored two of the goals and set up the third for Cédric, before substitute Nathan Redmond completed the rout late on.
Hasenhüttl was quick to pay tribute to the travelling supporters who he said showed his team the way to victory.
“You can hear our fans still singing – it’s unbelievable for us and very important for the fans,” he said. “I’m very happy for them.
“I’m very proud of my team and of the fans, because we had a really hard fight today.
“It was not easy, but I’m very happy that they showed us the way. I’m happy that we’ve reached the next round.
“For us all, it’s a fantastic evening. We will never forget this evening because you don’t win very often here 4-0, so it’s fantastic.”
Hasenhüttl admitted his team had to withstand some early pressure before making the breakthrough in the 21st minute, from which point Saints never looked back.
“It’s always tight against such an opponent, but if you score in the right moment – I think our first goal was our first chance – then everything can turn,” he added.
“I said to them at half time that we had to start the first 10 or 15 minutes better than we did in the first half, because if they get a goal it is really nasty.
“We tried to keep focused, going for the third and then the fourth, and that was the right way.”