Having failed to win since the opening day of the Barclays Premier League season, the Dutchman's position at the helm was looking fragile heading into the clash at Craven Cottage.
It had looked like their miserable run would continue as they stuttered against the Potters, but on-loan Darren Bent repaid Jol's faith with a late goal to secure a 1-0 victory.
"Relieved is probably not the word you use," Jol said. "You need results and you need to be in a good position.
"You need to be without pressure because any team under pressure won't perform as good as they are capable of. You saw that again today.
"Of course we were a bit lucky because if you look at Stoke, while they didn't create a lot of chances, Robert Huth had clear headers from set-pieces.
"You work on that the whole week but they still get the clear headers. We need to do better. We have conceded a lot of goals through set-pieces and that is the only thing that didn't happen, but they could have.
"So everything is good, but not for me. We have to improve on a lot of things but I am still a happy customer to get three points as that is what we needed.
"It was unbelievably important because I can come up with all the stories and excuses and say that we have got a good spirit and that they are behind each other and me or whatever.
"But if you don't get the points, then everybody is in a big depression.
"We are in the same depression now as many - seven, eight or nine - other teams, so that is good. That gives you relief and confidence again."
The latter's withdrawal in the 66th minute proved instrumental in deciding the result, with replacement Bent netting the winner.
"I was very happy with Darren Bent coming on for Berbatov, because if he would have stayed fit I would have probably left him on the pitch," Jol said.
"That was coincidence and it was great to have somebody like Darren Bent on the bench. He could have scored two."