Adam Lallana scored one goal and made two more for Guly Do Prado and Oscar Gobern as Saints won 3-0 at St Mary`s.
"I am pleased for my boys with the effort they put in and we kept going right to the end," said Yates. "Southampton are a quality side with good players all over the pitch and their class shone through.
"We were disappointed with the goals we conceded and to let in two headers is hard to take. It was always going to be hard for us to come and get anything from the game. Nigel had assembled a very strong team.
"We got off to the worst possible start and going 1-0 down after nine minutes. It was a mountain to climb. But we never gave up and created some chances of our own.
"If one of them had ended up in the back of the net who knows what might have happened. I wish Southampton all the best in the next round, we must now focus on the big game in the league against Southend on Tuesday night."
Source: PA
Source: PA