Darren Bent gave Villa the lead but Danny Shittu equalised before John Marquis headed a late winner at the second attempt.
Jackett told his side's official website: "I thought it was a terrific performance from the whole team tonight.
"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."
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