The Cottagers wasted a host of chances after going ahead through Steve Sidwell and were made to pay late on as the Baggies got a late equaliser to leave the Londoners in trouble
Jol, a former West Brom player, was left disappointed as Fulham had three goals disallowed – two efforts from Dimitar Berbatov and one from Hugo Rodallega – and Bryan Ruiz was denied by the crossbar.
The Cottagers' failure to build on Steve Sidwell's first-half strike proved costly as Gareth McAuley's injury-time header saw Steve Clarke's side snatch a point in the dying seconds.
"We should have won this game," he told reporters. "(Dimitar) Berbatov had two great chances – I don't think he was offside when he scored. The ball was in the net three times and it didn't count so we were a bit unfortunate.
"Especially when you saw the last 10 to 15 minutes, we looked a little tired. We had a few players on international duty.
"We looked okay, the balance was good, the shape was good."
Fulham have secured four points from their opening four Premier League games, with the club's solitary victory coming at Sunderland on the opening day of the campaign.
With Fulham's new owner Shahid Khan taking over from Mohamed Al Fayed, expectations are high among the club's supporters.
However, Jol has urged fans to be realistic about their expectations and has labelled the booing of his players following the final whistle on Saturday as "disappointing".
He said: "That is very disappointing. You come here to help the club and build something nice. If you look at the club, it is hard to fight the expectation levels.
"I can understand that they (the fans) want results, but that is what we want as well, we want to win games. You have to give the crowd what they want – excitement.
"It is very frustrating for us."