The Lions battled gamely at Wembley and in the match until Callum McManaman added to Shaun Maloney's first-half goal 12 minutes from time.
Jackett feels Wigan possessed some extra quality though and admits he was impressed by the contribution of Arouna Kone in midfield.
"I felt Wigan were good," Jackett said. "We had a very good 20-minute spell in the second half and had them on the back foot.
Their keeper made some good saves but we needed a goal during that period to build on. It didn't happen, they scored another on the break and that killed the game off.
"But we put in a sterling effort. Kone was excellent, though. He was something else and really brought their midfield into it and helped them score an excellent first goal."
The Millwall boss insists his charges must put the disappointment behind them as he prepares them for a Championship survival battle.
Jackett added: "That's the most important thing now. We would have loved to have gone one further but realistically we have to be proud of what the players have done to get this far.
"Now we have six games left before the end of the season and two in hand on almost everybody around us so we need to get some wins."