Hoops boss appeared to reject the offer from his Craven Cottage counterpart, but both managers said that it had been a misunderstanding following a demoralising loss for the hosts
Television images appeared to show Hughes rejecting a handshake from Jol following another defeat for his struggling side, who haven't won since their 3-1 victory over Wigan on January 18.
"I offered my hand, he shook it readily, I congratulated him on a good performance by his team, they won the game so I didn't have a problem with that," Hughes told reporters.
"I just took exception because I thought he was going to pat me on the head, which I deemed to be slightly patronising, so I brushed his arm away. That's all it was, it's no big deal. Make of it what you want," he added.
"Yeah, we did [shake hands]," Jol confirmed. "We shook hands after the game.
"Maybe I made it a bit too personal, you know. I tried to grab his shoulder, and he didn't like it because he's a tough guy. He's a winner. Maybe he doesn't like losing, I don't know. One of the two reasons."
Jol was understandably the happier of the two managers after his side's display, and was pleased with new centre forward Pavel Pogrebnyak, who grabbed his second goal in two games for the club to get all three points.
"I thought they wanted to take the game to us, and they were up for it. But we were up for it as well. We played some excellent football in the first 20 minutes.
"The first half was good after the sending off. They played in a different style. In a possession game you have to use everybody, you know, your full-backs as well and you have to find all the spare men.
"We didn't do that, and it's a lesson for next time. I feel that if we'd have scored the second goal, the game would have been over.
"We saw, probably from the first day [Pogrebnyak] was good. He's a good quality, holds up the ball. He's a good boy, wants to work. So we are very pleased that he came in after we sold Bobby Zamora.
"We have to get a settlement with Stuttgart, so it was a loan deal. After seeing him, yeah [I would like to keep him]. We took a risk and he took a risk. There's not a lot of players that will do that, you know - to come on loan to England. Hopefully he will keep on scoring goals and we'll see what happens in the next couple of months.
"I think [Pogrebnyak and Zamora] are a bit different. Bobby's more link-up play and he wants to be in the box on the end of crosses. They're two different number 9's.
"Stuttgart had four or five strikers so it was difficult for him. He knows after coming here, and I told him as well, that he would play, and that gave him a boost. [The goal] was good. The only thing was that he got booked [for celebrating], maybe that's something he's got to learn.
"Bobby wasn't desperate to get out of the club. They [QPR] made him an offer and they made us an offer. The same as they did with Andy Johnson. We didn't accept the offer for Johnson, but we did for Zamora."
Jol was, however, upset when Adel Taarabt waved an imaginary card at the referee after Moussa Dembele brought down Joey Barton having just been booked.
"I think that [Taarabt miming the issuing of another card] was wrong because you can see that the referee thought it wasn't enough to book him again and have him sent off.
"The referee saw it, it wasn't enough for him, so leave it at that. It's a South American thing, you know. I don't like it."
Hughes didn't go as far as defending his player for the action, but did add that he believed Dembele should have been red-carded, especially considering Samba Diakite, QPR's debutant, was sent off for two bookable offences just after the half-hour mark.
"I didn't see [Taarabt waving the card]. We know it happens. Some players do it, some don't. Some manager shout and bawl, I do, and others wave cards. But we all shout and scream the same.
"[Dembele] should have been sent off because it was a second yellow - he cynically pulled him back. At the moment things are conspiring against us, but on another day he would have got sent off, things would have been evened up and we'd have made more of a game of it. But the referee deemed that it wasn't worthy of a sending off. The actual incident was certainly worthy of a second booking.
"I don't think [our] discipline was too bad. Obviously because it was his debut [Diakite] wanted to make an impression, he was enthusiastic. I don't think he was reckless, he just mistimed challenges.
"Unfortunately for him, he doesn't know the league as yet. In fairness, I take responsibility for that. In an ideal world, you want to introduce him to the Premier League a little bit more slowly, but given our circumstances, we need good players on the pitch.
"Up to the point of his sending off I thought he was excellent and arguably our best player at that point. Obviously we need to keep the full complement of players on the pitch, because if we don't it's going to be very difficult for us. We haven't managed that in our last two home games so it's pretty obvious where our problem lies."
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