Southampton goalscorers Graziano Pelle and Steven Davis conceded there was room for improvement after the 2-0 Premier League win over AFC Bournemouth.
Pelle headed home Dusan Tadic's 36th-minute cross five minutes after Davis had volleyed in to crown a superb team move.
Bournemouth conceded five goals in each of their previous two league defeats against Manchester City and Tottenham and another thrashing appeared to be on the cards.
But Eddie Howe's team made most of the running after half-time, with Southampton losing Victor Wanyama to a second yellow card as their opponents struggled to turn possession into clear-cut chances.
"Second half was completely another game," Italy striker Pelle told Sky Sports.
“We were good, to keep strong as a defensive line, we worked hard because they were trying to reduce the gap.
"We have to improve in some parts when we are winning 2-0 - we need to keep going.
"Maybe up front we need to be stronger to keep the ball."
Northern Ireland midfielder Davis felt he and his team-mates could have been sharper in possession after the interval.
"We were very happy with how we played first half and knew they were going to come back at us," he said.
"Credit to the way they came out in the second half but we've got to look at it ourselves as well.
"We've got to do better in possession. There's things we can improve on but I'm delighted to get the three points and keep a clean sheet.”
Pelle embarked upon a Haka-style goal celebration with Southampton's sports therapist Graeme Staddon, whose New Zealand compatriots claimed Rugby World Cup glory against Australia on Saturday.
"Our physio is from New Zealand and it was a good day for him," Pelle explained.
"It's just a reward to him because he was feeling a bit lonely in this country.
"I said 'okay, I'm going to come to you'. I'm still Italian but he is my friend and he deserves it.
"He was believing in me too that I would score. It was nice for him."
