First-half goals from Scott Golbourne and Kevin Doyle put Wolves on course to secure five straight league wins for the first time since 2008.
But Swindon wasted a host of chances, being frustrated by goalkeeper Carl Ikeme, until Dany N'Guessan struck in the 82nd minute.
Kevin Foley then restored Wolves' two-goal advantage before Ryan Mason struck from long range in a tense finale.
Jackett said: "We certainly didn't have everything our own way. After going 2-0 up, we didn't defend well enough as a team.
"It always looked like Swindon would come back into the game and on the break we needed to be more incisive.
"We didn't do well enough with our passing because there were a lot of holes against a Swindon side who were coming at us from all angles. So there is plenty improve on.
"I am pleased with the win and the table is taking shape. But the fact that my goalkeeper was probably my best player does show how the game went for us. We must not be fooled.
"We need to do better than we did. We are pleased with the win and with the three goals because if you can score goals consistently then you can usually pick up points.
"But defensively there is work that we have to do where we give up territory and we give up possession too easily and we need to be harder to break down then we were today. We have to keep working but capitalise on the good things that we have."
Wolves quickly took control of affairs but there was some good fortune about Golbourne's first goal for the club following last month's B£700,000 move from Barnsley.
His third-minute high ball into the box was meant to be a cross but it drifted towards goal and completely deceived keeper Wes Foderingham, who was left somewhat embarrassed as the ball drifted over his head and into the corner of the net.
Swindon could easily have wilted after that early setback but it was they who then dominated proceedings only for Mason and Alex Pritchard to be denied by Ikeme.
Failure to convert their chances cost Swindon dearly two minutes before half-time when Doyle released Leigh Griffiths and then raced into the area to convert a cross from the Scotland international with a far-post header.
Mason then failed to take any of three gilt-edged chances that came his way in a six-minute second-half spell - including one that hit the post - before N'Guessan showed him the way to goal, ironically from a pass by Mason.
Foley then looked to have made the game safe when he met a cross from Bjorn Sigurdarson, only for Mason to set up a thrilling finale with an unstoppable 30-yard drive.