Ronald Koeman was left to rue a poor first-half display and recognised Stoke City created the better openings in Southampton's 1-0 Premier League defeat on Saturday.
Bojan Krkic's clever flicked finish in the 10th minute was enough for Stoke to win at St Mary's Stadium for the first time.
Stoke's margin of victory could have been bigger, with Xherdan Shaqiri guilty of missing two particularly good chances, while substitute Ibrahim Afellay had a shot cleared off the line in the closing stages.
A second-half rally failed to produce clear-cut chances for Southampton and manager Koeman expressed his disappointment at their slow start.
"It was not good enough in the first half. In the second half, we played better, it was a good reaction, but I have to recognise that best chances in the game fell to Stoke," he told BBC Sport.
"We created some good chances but they were dangerous on the counter-attack.
"They had a very good organisation in defence and you have to have very good quality on the last pass, the last cross, and we didn't bring that."