Jones made the £17million move from Blackburn to Manchester United in the summer and quickly established himself as a regular centre-back at Old Trafford.
Injuries to Rio Ferdinand and Nemanja Vidic at West Brom on the opening day gave him his initial chance - and he has not looked back since.
He earned his first England call-up last month for the games with Bulgaria and Wales but got his playing breakthrough in Podgorica at right-back and looked equally at home.
A 2-2 draw was sufficient to seal England's place at the top of their group despite the sending-off of Wayne Rooney thanks to goals from Darren Bent and Ashley Young.
Cahill, who played inside Jones at centre-half, said: "I thought Phil did really well, he got forward when he could, he defended well in really difficult circumstances.
"It was a hard game for him to get his first cap. It was a big game and conditions didn't help him.
"But he has already looked at home with Manchester United this season since moving there.
"He did really well in Montenegro. He really stood up to the task and seeing youngsters coming through and doing well is great for England.
"I think we are in really good shape. We've got young players coming through now with a blend of experience as well.
"That will stand us in good stead for the tournament and a couple more games before we get there. I think we will do really well."
Cahill accepts Rooney's absence through suspension for at least the opening game of Euro 2012 will be a big blow to England's hopes.
But he praised the way England dealt with his departure against Montenegro, who have qualified for the play-offs as runners-up in the group.
He said: "It will be a massive blow with the talent Wayne has. He is phenomenal. It is going to be a big blow at the finals.
"Going down to 10 men was tough but the main thing was we got the job done in difficult circumstances.
"When something like that happens, you've got to deal with it and carry on and that's what we did.
"I hope everyone sees it as a job done. We've done terrifically well to get to the tournament and we are looking forward to it now."
Skipper John Terry hopes England can learn the lessons of the 2010 World Cup finals in South Africa.
Having been built-up prior to the tournament, England limped through the group stage before being sent packing by Germany.
He said: "I think we always can challenge. We clearly have to learn from where we went wrong in South Africa.
"It doesn't give us the God-given right to go out there, just because we've changed things, to win it.
"We still need to put in the hard work on the training field and the matches in the meantime."