LONDON-- West Ham United missed out on a fourth successive Premier League victory as the festive fixtures concluded with a drab 0-0 draw at home to Brighton & Hove Albion on Tuesday. Brighton would have moved above West Ham into sixth place with a victory but chances were few and far between at the London Stadium with a point apiece a fair outcome. Pascal Gross should have put Brighton in front shortly before halftime but his header was saved by Alphonse Areola while Adam Lallana went close to a late winner. Pablo Fornals should have done better for the hosts after the break and Tomas Soucek also prodded an effort wide. In the end West Ham, without African Cup of Nations-bound Mohammed Kudus and injured fellow midfielder Lucas Paqueta, appeared content to take the draw which left them in sixth spot with 34 points from 20 games. Brighton's first clean sheet of the season in the league moved them above Manchester United into seventh on goal difference with 31 points. While the game will not live long in the memory, both sides can embrace the New Year optimistically with European honours still possible and a challenge for a top-six place in the Premier League. "It was disappointing from our point of view because I think we controlled the game and created enough chances," Brighton's 37-year-old midfielder James Milner told Sky Sports. "But it was a solid performance especially with a couple of boys coming back who haven't had too much football." The evergreen Milner was making his 632nd Premier League appearance to move level with Ryan Giggs and only Gareth Barry (653) has played more matches in the competition West Ham won the reverse fixture earlier in the season -- ending a 13-match winless streak against Brighton. But they could not earn a first top-flight win at home against the south-coast club since 1983. "We had a couple of chances. Tomas Soucek had a great chance," West Ham boss David Moyes said. "We rode our luck a wee bit. It's been a really good Christmas period, three wins and a draw. No complaints."