It's now four league games in a row without a win for Everton.
Carlo Ancelotti's side have seen their Champions League hopes fade further away after a frustrating scoreless draw away to Brighton in the Premier League.
They're now 8th in the table, seven points off fourth place West Ham.
Everton captain Seamus Coleman remains determined to fight for some form of European qualification next season
West Brom remain second from bottom, but they won for the second game in a row.
Republic of Ireland international Callum Robinson scored once again, as Sam Allardyce's side won 3-0 at home to Southampton.
West Brom are still eight points from safety, with seven games left to play in the season.
Manager Sam Allardyce was delighted with the way his team followed up their impressive 5-2 win at Chelsea last time out
