Stuart Armstrong was happy to score his first Southampton goals, but frustrated they did not lead to three points at Fulham.
Saints are still without a win since September 1, adding to the pressure on boss Mark Hughes, who has three wins in 21 Premier League games since his appointment in March.
Armstrong's performance and two goals provided a positive in Saturday's 3-2 loss at Craven Cottage, but the Scotland midfielder rued the defeat.
"That's what I've come here to do – create and score goals," Armstrong, a summer signing from Celtic, said on southamptonfc.com.
"I'm glad I'm up and running in that sense, but I want the goals to mean something. It's about the team getting as many points as we can."
Hughes, whose side face Leicester in the Carabao Cup on Tuesday, had to withdraw Armstrong with 10 minutes remaining due to cramp, but was pleased with his display after an indifferent start to life in the English top-flight.
Hughes said: "Two great goals. The second one was exceptional.
"It's been a little bit difficult for him coming into a new league. He started well, then his form plateaued a little bit, so he went out of the team.
"He's come back, he's in confident mood. He's had a good couple of games for us, went away with Scotland and acquitted himself really well.
"He's in a confident period, so we'll reap the benefits of that. He looks a really accomplished player now."
Aleksandar Mitrovic scored twice and Andre Schurrle was also on target for Fulham in a win on Claudio Ranieri's debut as boss.
Ranieri is demanding improvement, though, particularly defensively.
Fulham are the only one of the 92 English league sides not to have kept a clean sheet this season after Macclesfield kept out Yeovil in League Two on Saturday.
Ranieri said: "I ask just this: never, never give up. Work hard until the end, at the end we'll see the result.
"It was a good match. Southampton had a chance to score a goal (to draw). Sergio Rico made a fantastic save.
"That is no good. Because I want less chances for the opponent. It's good for Sergio. But it's not good as a manager. Too many chances."
ga('create', 'UA-72310761-1', 'auto', {'name': 'pacontentapi'});
ga('pacontentapi.set', 'referrer', location.origin);
ga('pacontentapi.set', 'dimension1', 'By Matt McGeehan, Press Association Sport');
ga('pacontentapi.set', 'dimension2', '36049953-9f10-496f-866e-ceba4faf12fc');
ga('pacontentapi.set', 'dimension3', 'paservice:sport,paservice:sport:club-news,paservice:sport:football');
ga('pacontentapi.set', 'dimension6', 'story');
ga('pacontentapi.set', 'dimension7', 'composite');
ga('pacontentapi.set', 'dimension8', null);
ga('pacontentapi.set', 'dimension9', 'sport:football');
ga('pacontentapi.send', 'pageview', { 'location': location.href, 'page': (location.pathname + location.search + location.hash), 'title': 'Armstrong frustrated his maiden Saints goals couldn\u2019t prevent another defeat'});
