The Championship side fell behind to Darren Bent goal on 22 minutes but ran out winners thanks to Danny Shittu's equaliser (27) and John Marquis' 89th minute winner.
"It was a fantastic night," said Jackett. "The crowd generated a great atmosphere and I'm very appreciative of the way they drove us on. The link between the players and the crowd was a big one.
"I thought it was a terrific performance from the whole team tonight.
"To a degree, we had some players playing out of position and a slightly imbalanced team.
"We persevered after going behind and did well to come back from an early goal. I thought Andreas Weimann's acceleration to go past Shittu was excellent and then (Darren) Bent found the finish.
"We got a goal back from a set piece which we've been poor from this season, with the quality of our delivery from James Henry. We should score more goals from corners.
"I thought we deserved to win and I was so pleased for John Marquis that he got the winning goal. He has been out for a long time and has worked so hard to get back to fitness."