Slaven Bilic admitted Albion didn't do enough to take all three points at Swansea after his side's first 0-0 draw of the season.
In game of few chances, Callum Robinson and Jake Livermore came closest to giving Albion all three points.
Bilic was satisfied with Albion's performance at The Liberty Stadium but reckons they will have to improve if they to win games between now and the end of the season.
"We aren't over the moon, but it's a tough place to come because they have a team who have been very unlucky with recent results," said Bilic.
"It's good to get the clean sheet with a solid performance and to more or less control the game, but we know have to be better in terms of quality in the final third. That's what was missing today.
Albion's draw and Leeds' victory over Huddersfield saw United leapfrog the Baggies at the top of the table.
But Bilic isn't too concerned about his side being knocked off the top spot with a six point cushion over third-placed Fulham.
"I would love to be on the top spot but it doesn't worry me," he said.
"The results apart from Leeds and Brentford were okay. At this stage of the season, the results around you affect the valuation of the point.
"Considering the bigger picture, this was a good point."