A returning David Moyes would have been hoping his side could take the momentum they had gained from their home draw with Leicester City last Friday with them to Merseyside, however, the Hammers fell well short and were considerably off the pace.
Jordan Pickford saved Manuel Lanzini's spot-kick after Ashley Williams' challenge on Diafra Sakho just before the hour mark, and, after Rooney's outrageous effort from distance, Williams then added a header with 12 minutes of normal time to go.
"As David Unsworth said, we've been hurting".
"Every player was committed".
Sam Allardyce is seen arriving at the stadium prior to the match
It's five weeks since the Toffees dismissed Dutchman Ronald Koeman thanks to a poor run of form that saw them slump to third from bottom in the Premier League. I'm delighted for the club. With just about their first risky attack of the game, Gylfi Sigurdsson played Calvert-Lewin in one on one with Joe Hart, and the England 'keeper came flying out of his goal, bringing down the young forward as he dived for the ball.
However, the deal could be done by the weekend - a fact David Unsworth appeared to acknowledge. "Goodison must be a fortress for the rest of the season if we are to finish in the top half".
Allardyce will take the reins for the first time against Huddersfield on Saturday.
Having had nearly two full days less to prepare for this fixture following Sunday's 4-1 thrashing at Southampton, David Unsworth made five changes for his final game in caretaker charge of Everton.
Allardyce is an ambassador for bookmakers Paddy Power, who have worked closely with the ex-England manager throughout this season.
'Destiny 2' free trial to kick off this week
Player progress will be restricted to level 7, but characters will carry over to the full game if and when it's purchased. Bringing it down to the point where you are only getting four percent of the XP you should be getting.