Fulham boss Chris Coleman switched to a 4-4-2 formation for this tie and the line-up gave them greater numbers up front.
However, their attacking threat – which peaked when Carlos Bocanegra hit the post with a freakish 28th-minute attempt – became almost non-existent as this game wore on.
Coleman, who has mounted many passionate defences of his team this season, finally snapped after the game and laid into his players.
He fumed: “We were inept. There are no excuses for that performance. We were dead lucky and could have come off losing 2-0 or 3-0.
“We were poor again and without van der Sar – who had a terrific game – we would be out of the FA Cup and I couldn’t have had any complaints.
“Edwin was far too busy and it’ll be harder at Upton Park.
“The thing is that wasn’t even West Ham’s strongest team. They had a lot of players missing.”
Promising to wield the axe, he went on: “A couple of my players looked complacent. We’re in a good position in the league and maybe they think all they have to do is turn up.
“They might think they’ve done enough already this season but we’re at a critical stage and going through to the next round of the cup is very important to us.
“I had some strong words after the game and now it’s up to me to shake it up.”
The London rivals both go into the hat for Monday’s quarter-final draw but meet again on February 24 for the right to advance along the road to Cardiff.