Gatland was speaking after his team had been beaten 19-16 by South Africa, who now face Jones’s men on Saturday in a repeat of the 2007 showpiece.
Meanwhile, Wales face the All Blacks in the bronze final 24 hours earlier – which was Gatland’s last match as boss.
“Well, guys, can you just send my best wishes to Warren to make sure he enjoys the third and fourth place play-off?” Jones said at a press conference.
Jones and Gatland are long-standing sparring partners and the outgoing Wales boss made a pointed remark about England’s crushing win against the reigning world champions.
“We have seen in previous World Cups that teams sometimes play their final in semi-finals and don’t always turn up for a final,” Gatland said.
“So it will be interesting to see how England are next week and it could be a good game.”
Jones has delivered a major boost to the nation’s hopes of winning a second World Cup by declaring Jonny May has recovered well from the dead leg sustained in the 19-7 rout of New Zealand.
The Leicester try machine was touch and go to face the All Blacks because of a hamstring issue and having recovered from that, he lasted 45 minutes before suffering an additional injury setback.
“We had a walk through this (Monday) morning and we had to tell Jonny to slow down a bit,” Jones said.
“He’s probably in better condition than he was last week at this stage. Immeasurably better.”
Owen Farrell also incurred a dead leg in the first-half of arguably the greatest victory in English rugby history but he managed to finish the match, albeit while handing the kicking duties to George Ford.
“Owen’s a bit sore but he’ll be fine. We’ve got a few others carrying bumps and bruises because it was a tough old game,” Jones said.
“It’s great – you give the country something to cheer about and with Brexit at the moment they probably need something to cheer about,” Jones said.
“It’s the job of a team to make the country happy and we’ve made the country happy. Not as happy as they can be because there is still a game to go as we’ve said.
“The crowds here generally in the World Cup have been fantastic and I thought our supporters on Saturday night were massively instrumental in helping us get home.
“Their singing and their general support of the team has been outstanding. We urge them to keep doing that.”