Wolves put the result beyond doubt after a dominant first-half display when Griffiths, Lee Evans and Bakary Sako were all on target.
Scotland international Griffiths then grabbed a second-half penalty as he opened his account for the club after scoring 28 goals on-loan for Hibernian last season. Jackett said: "We feel that if we can get our play right, get our passing right, and if we create, that Leigh Griffiths will put the finishing touches to it.
"If we can create chances like we did here then he is capable of putting those finishing touches to it.
"I'm sure he's delighted to get off the mark in his Wolves career in the first home game. Getting such an early goal in a game such as this is key, for both him and the side.
"I've found him fine in the month-and-a-half or two months that I've seen him. I got the job one day and phoned him the next and that's how I feel, having watched him last season.
"I told him 'You're not moving, you're coming back to Wolves and I'm going to give you a chance. You're going to play'. That's what he wanted, that's what every player wants and hopefully now that backing can be repaid."
It was Jackett's first win and he hopes a marker has been laid down.
He added: "I've been looking for things to settle down now after basically pulling it apart.
"It was needed but now we need to try to get some continuity and for the side to just settle down and get a feel for each other.
"The supporters have wanted to see a new team, see some attacking play and some quality and, when needed, see the players roll their sleeves up and battle and scrap, if it's possible to have all those things.
"The group of players shouldn't get carried away but they should be encouraged by the standards they set and should also be able to build on that going forward."