Midfielder Dale Stephens insists Albion have enough in their squad to stay up - whether the club sign a striker in January or not.
Brighton missed out on adding a forward in the summer transfer window, when moves for Florin Andone and Vincent Janssen fell through on the final day.
Glenn Murray and Tomer Hemed have since scored crucial goals, with five and two respectively, to help the Seagulls reach 21 points after 20 Premier League games.
Albion are 12th in the table and Stephens said: "Our start probably surprised a few people but I don't think we surprised anyone in-house.
"We know what we're capable of, the manager is obviously happy with the squad and the players we've got.
"We've got a good enough squad to compete at this level already. If a striker does come in January to strengthen, then that would be great but I believe we're got a strong enough squad already."
Albion travel to 15th-placed Newcastle tomorrow, before hosting third-from-bottom Bournemouth on New Year's Day.
Stephens said: "It's a big period for us. We knew Christmas would be a tough period but we got a good result (against Watford) and go into this period still confident of what we can achieve.
"Consecutive games can mean consecutive points as well. It's six points to play for in the next two games and hopefully we can do the job."