After just two wins in 15 Barclays Premier League games, there have been growing rumbles of discontent from sections of the west Londoners' support base.
However, that air of tension has begun to dissipate over the last 24 hours, with news the club has become debt-free followed by a 3-1 win over the Hammers.
Dimitar Berbatov celebrated his 32nd birthday with a vital - if offside - opening goal, although Kevin Nolan levelled for the visitors at the start of the second half.
The Whites rallied and regained the lead a minute later through Hugo Rodallega, before Joey O'Brien turned in a Mladen Petric shot in stoppage time.
"The result was very important," Jol said. "It was a vital, vital win.
"They were on 27 points, we had 25. Norwich were on 26 so it is a vital win.
"I am a happy customer, especially is you saw this game and the last four games here at home.
"We lacked a bit of luck, sometimes a bit of quality and today [Wednesday] the first half we were good.
"We were happy to score that goal, although I've heard it was irregular but I am not sure.
"Maybe it was offside but I can remember a couple of moments this season when we had the same decisions against us so, as you say in England, you win some, you lose some.
"Hopefully today [Wednesday] we won some and that was probably the case with the first goal."
The only bad news on Wednesday night was injury-related, with Jol revealing Berbatov requires a scan on a hamstring injury.
However, Philippe Senderos is fine despite limping through the final 10 minutes, and Jol expects new arrivals on Thursday.
AC Milan's Urby Emanuelson and PSV Eindhoven right-back Stanislav Manolev are closing in on a move to west London, while there could be a few other additions.
Asked if he was close to signing the former, Jol nodded and said: "It is a loan until the end of the season. It is not easy to get players from AC Milan on a permanent basis.
"I coached him at Ajax. He is a skilful player, very agile. He is very mobile, quick.
"He can play left midfield, wide, play number 10 so I feel we need fresh legs."
West Ham are also hoping to be active before the deadline, with Blackburn goalkeeper Paul Robinson one of those on the east Londoners' radar.
"We've obviously worked with him before and know what he is about," assistant manager Neil McDonald said.
"We will see how it goes. It is just paper talk at the moment but we will see how it develops over the next 24 hours.
"Sam (Allardyce) is working very hard behind the scenes. If we can bring anyone else in, that would be great. It would be more competition for places."
McDonald, attending the press conference in place of manager Allardyce, cut a frustrated figure after what he felt were several poor decisions.
"We've conceded the first goal, which is offside," McDonald said. "That is very, very disappointing and sometimes that knocks the stuffing out of you.
"We're expecting to get that decision right. It was not just one person but three people offside. It is not second or third phase either - it is the first phase.
"That puts us on the back foot but I thought we showed tremendous character to come back in the second half.
"We put Fulham under pressure and created some really good chances.
"We got back into the game and then disappointingly conceded within a minute.
"It is always difficult in the Premier League to come from behind but we still pushed forward and I think we should have had two penalties as well so I think we were a little harshly done by today [Wednesday].
"It is difficult in the Premier League but when you don't get those decisions going for you it is doubly disappointing."