Andy Carroll said West Ham were eyeing European football after scoring in a 3-0 win at home to Hull on Sunday that took the Hammers into seventh place in the Premier League table.
Second-half goals from Carroll, Morgan Amalfitano and Stewart Downing secured all three points for the east London club in front of the Upton Park home crowd following a run of four games without a win,
Defeat saw Hull -- punished for failing to take advantage of their early chances -- remain in the bottom three, still a point from safety.
Asked if West Ham could qualify for Europe, England striker Carroll told Sky Sports: "There's a belief in the dressing room, I don't see why not.
"We haven't had a win in the last few games but we've had the performances that can take us up to the top."
After a goalless first half, the Hammers took the lead in the 49th minute when Hull goalkeeper Allan McGregor could only tamely parry a shot from Enner Valencia and striker Carroll got in front of the covering defence to seize on the loose ball from close range.
Valencia thought he had made it 2-0 in the 57th minute after running on to a fine pass from Alex Song but his 'goal' was disallowed for offside, although replays suggested he was level.
But the hosts doubled their lead through Amalfitano, who scored five minutes after being sent on as a substitute for Mark Noble by Hammers manager Sam Allardyce.
Valencia was again the provider, his pass finding Amalfitano, who then produced a sublime finish to chip McGregor in the 69th minute.
West Ham then piled on the agony for Steve Bruce's visitors three minutes later when Song's 45-yard pass through the middle evaded the Hull defence completely, allowing the onrushing Downing to finish with aplomb.
Five minutes from time, West Ham almost made it 4-0 but Kevin Nolan's shot came back off the crossbar.
It might have been a different story had Hull turned their early opportunities into goals.
They should have been ahead when Sone Aluko, whose pace repeatedly caused problems for the West Ham defence, produced an excellent cut-back only for Ahmed Elmohady to drag his shot wide.
Aluko then carved out an excellent opportunity for himself after going past James Tomkins on his way into the box but the Nigerian lingered too long over his shot and gave James Collins the time to block his shot.