Australia completed an 87-run victory in the third and final Test against West Indies on Monday at Kensington Oval.
West Indies, chasing 475 for victory, were dismissed for 387 in their second innings about 25 minutes before tea on the fifth and final day.
"I am proud anytime we win a Test because it's not an easy thing to do," Ponting told reporters.
"Winning a Test match is hard work. All the guys at the moment are sitting back there in the dressing room exhausted. It has been hard work this whole series, and winning these two Test matches.
"For Brad Haddin and Beau Casson, playing in a winning Test match team and series winning teams for the first time, it will be a step in the right direction for them.
"West Indies is a good place to play cricket, although we have not had the crowd we may have wanted, but all three Tests have been entertaining."
Australia won the three-Test series 2-0, after they also won the opening Test at Sabina Park in the Jamaica capital of Kingston by 95 runs.
The second Test at the Vivian Richards Cricket Ground in the Antigua villageof North Sound was drawn.
The Aussies have already retained the Frank Worrell Trophy - symbol of Test supremacy between the two sides - but they were pushed all the way by West Indies.
This many people is evidence that the era of their dominance of World cricket is ebbing away, following the retirement of several high-profile players, most notably Shane Warne, Glenn McGrath, and Adam Gilchrist.
"I actually said when some of the more senior players moved on that I felt it was going to be one of the more exciting periods in my career to have some new, fresh faces around the team," Ponting said.
"I thought it was going to be exciting, and it has been, it has been great. I have enjoyed it. I have enjoyed having guys making their debuts and guys who have played a handful of Tests in the side because I feel I have a lot to offer to those guys by way of experience and know-how in certain situations in games.
"If I can go and say one thing to them that is going to help them out in situations in games, I feel that's my job. I am really enjoying it, and I do not think it is hindering me.
"I felt as good in this series as I have felt for a long time. . .It's a different time for the team, but we're winning games and this is something about which I am pretty happy."
Ponting noted that his side learned quite a lot from the series, particularly ahead of their next Test tour to India.
He indicated that some of the conditions in which the series was played were identical to the sub-continent, and it has taught his side the value of patience.
"There are lots of positives there for us, but we're probably not demolishing sides like we might have two years ago, but we are grinding teams down and winning Test matches, and we're doing it well.
"It's the style of play more than anything else. You have to accept that the game may go into the fifth day and you have to be patient. You have to grind an innings out, or in the middle of a bowling spell, not try to attack too much.
"When you attack too much, runs begin to flow, and the batting team gets momentum in the game, and it starts slipping away from you.
"That's one area I think we have improved in vastly over the last four or five years, and it's our knowledge about how to play in these types of conditions, we have learnt about how to play in them."
Australia now face West Indies in a Twenty20 International on Friday at the same venue before beginning a five-match One-day International series on Tuesday June 24.