The two sides went into half-time level at 0-0 at Craven Cottage, but former Aston Villa striker Bent wasted two clear-cut chances, first with a back-post header before crashing an effort against the post.
Swansea made Fulham pay for their wastefulness in the second half as an own goal from Aaron Hughes and a sweet strike from Jonjo Shelvey sandwiched Scott Parker's fortunate cross-shot.
The loss was Fulham's fourth straight defeat in the Premier League, leaving them in 18th position in the Premier League, leading to some supporters once again chanting for Jol's dismissal.
But the Dutchman feels Fulham were unlucky in defeat.
"Darren Bent could have scored a hat-trick and we should have been up, but it didn't happen," the Fulham manager told BBC Sport. "The own goal was tough on us and we could have been up at half-time.
"If you don't score, you can't win games. They had players missing and we had the chance to beat them. You have to take the opportunities in this league and we didn't.
"All the hard work we've done in the last two weeks we haven't built on it.
"I want the fans to realise that Swansea are a good team and we were unfortunate. A win would have put us above them and it was close."
'He already had the ability but didn’t use it because he was afraid to shoot – I said, "You’re a player who has to decide games – you have to take risks, mate"': Liverpool star was forced to become confident by team-mates
‘Diaz is often our most dangerous guy for the full 90 minutes, every time I’ve seen him’: Liverpool legend makes shock claim about the Reds' attack
