Iliman Ndiaye scored twice on his full debut as the Blades secured their first win of the Championship season with a clinical display at Bramall Lane.
Ben Osborn also hit a brace for Sheffield United, with Morgan Gibbs-White - on his first appearance for the club - and John Fleck also on target.
Jack Marriott and a Jonson Clarke-Harris penalty were mere consolation for Posh.
It was a fourth game without a victory for Peterborough and left them just one place off the foot of the fledgling table.
Jokanovic said: "The team showed their personality. We didn't change anything in the second half, we pushed harder and ended up finding the benefits in the game.
"We tried with some different qualities and characteristics, (Iliman) Ndiaye scored two goals, (Morgan) Gibbs-White scored one. They had enjoyment to play the game which I believe our supporters enjoyed watching them. I must be satisfied.
"After a depressing start to the Championship, we needed this kind of victory and the most important thing for me is that my team are starting to trust that they are good players and that they can win games.
"I was talking with (John) Fleck this week. I was explaining what our expectation was from him. Billy Sharp was brilliant today, too. He was running I don't know how many times into space. He didn't score today but he created a lot of problems for the Peterborough defence."
Peterborough boss Darren Ferguson bemoaned his side's poor defending.
Ferguson said: "We felt on the counter-attack, we would cause them problems, which we did at times. The first five or 10 minutes of the second half was our best period, Jack (Marriott) missed a very big chance at 1-1.
"The manner of some of the goals were very disappointing. Regardless of what level, you can't lose goals in the manner that we did today.
"I must get them going again because we've got another game on Tuesday, games come thick and fast after the international break which is always a positive.
"We had them where we wanted them, they conceded from their point of view a soft goal and their fans were getting edgy because they expect wins. But the opposite effect happened when they went 2-1 and 3-1, their confidence went through the roof.
"When you play against good players, which they are, they are quality players, there is certain things you have to do to make it as difficult as possible for them."