Hayden Mullins' own goal put the Bluebirds ahead before the interval and Jay Bothroyd's sixth goal of the season put game to bed four minutes into the second period of a 2-0 victory.
The win sees Cardiff in second place with 10 points from their four games and Jones believes a promotion assault is on the cards.
"We worked hard and that is where the goals came from. We ground them down," he said.
"We have got new players coming in and it takes a little bit of time to get it right but it was a professional performance from us.
"Portsmouth still have Premier League players and we knew we would have to work for the victory.
"We are changing the culture at the club and we have raised the bar. You have to do that when you bring good players in.
"In previous years we have had to sell our best players but this season we have kept them and added to the squad and that has changed expectation levels.
"I have had success wherever I have been and I have had success here. I am just trying to do my job.
"The fans have had some good times here and hopefully I can make this another successful season for them."
Portsmouth manager Steve Cotterill was left to bemoan his side's lack of firepower as they prop up the rest of the division with just one point.
He said: "We gave away two silly goals and that sums up the way things have been going for us for the past eight weeks.
"The trouble is if someone scores twice against us we do not have the firepower to come back.
"We are bottom of the league and the alarm bells are ringing but I was ringing them from the first day I took the job.
"I always knew this was a tough job and no-one will ever know just how tough it is because I won't tell them because if I give in then everyone will give in.
"This is still a great club and we have to make sure we get things right on the pitch.
"I am a fighter and I will keep fighting but as a manager you need the tools to be able to do your job to the best of your ability.
"It concerns me we will lose players before the transfer window closes."