The midfielder, who plays for English Premier League side Blackpool, sent a blistering left-foot strike past keeper Diego Barreto in the 53rd minute after the ball dribbled into his path off the back of Richard Garcia.
"I just hit it really and I think I got a bit of a swerve on it before the keeper and (am) just happy it went in," Carney said in a televised interview.
"Overall I think we deserved the win as well and we looked very positive."
The strike was cruel for Barreto who had made a number of fine saves early as the Socceroos dominated the first half.
The win gave new coach Holger Osieck his second win from three starts since taking over after the World Cup.
Although missing skipper Lucas Neill and midfielder Brett Emerton, Australia fielded a strong line-up with Tim Cahill and Harry Kewell starting and goalkeeper Mark Schwarzer wearing the captain's armband.
Paraguay were without Oscar Cardozo, Bundesliga forward Lucas Barrios and Manchester City's Roque Santa Cruz but appeared the more fluid side early on with striker Nelson Valdez lurking dangerously near the box.
The South Americans launched the first genuine attack when Valdez pounced on a cross into the box and tested Schwarzer with a stinging strike in the 13th minute.
BLISTERING STRIKE
Although disorganised in defence, Australia hit back with their own chance nine minutes later, forcing Barreto to save a sharp header from an unmarked Cahill off a corner kick.
The Paraguay keeper then parried away a blistering strike from Jason Culina and Josh Kennedy headed wide from a Luke Wilkshire cross for the Socceroos' third shot in a minute to leave the Paraguay defence reeling.
The South Americans survived to the break as their opponents blew chances with messy passes and poor decision-making.
Valdez tested Schwarzer again in the 54th minute and substitute Cesar Benitez brought the keeper off his line 13 minutes before time in a nervous moment for the Australia defence but the Socceroos held on.
"I think it was a well deserved win," said Osieck.
"I think in the first half we created a lot of good opportunities but unfortunately we couldn't convert (them) and sometimes it happens in football that you have to pay for it, but it didn't happen today."
