The battle for the final Champions League qualifying slot is wide open this season but the four clubs best-placed to fight it out all faltered over the weekend.
Tottenham Hotspur currently occupy fourth on 38 points but they missed an opportunity on Saturday when they were held 0-0 at home by Hull City.
Manchester City are fifth, also on 38, after they lost for the first time under Roberto Mancini - 2-0 at Everton - with Villa sixth on 36.
Liverpool, "guaranteed" a top four finish by manager Rafa Benitez, are seventh on 34 after they drew 1-1 at Stoke City.
Chelsea still lead the way on 48 points following their 7-2 demolition of Sunderland, with Manchester United on 47 after their 3-0 home win over Burnley.
Villa's challenge lost its way with defeats by Arsenal and Liverpool at the end of December and they looked short of inspiration against a West Ham side who started the day in the relegation zone.
Villa played on Thursday when they beat Blackburn Rovers 1-0 away in the first leg of their League Cup semi-final and that perhaps contributed to their lack of sharpness.
Ashley Young, Gabriel Agbonlahor and Stewart Downing all had half-chances as Villa made most of the running but West Ham, who have won only one away league game this season, were well organised at the back and generally coped well.
Goalkeeper Rob Green was rarely tested but was quick off his line in stoppage time to smother at the feet of Agbonlahor when the forward was sent through by John Carew's flick.
