The Cherry & Whites came from 14 points down at half time to win 30-16 at Old Trafford, adding to what has already been a memorable year following victory in the Challenge Cup.
"When I got in at half-time, the players were already talking about what they had to fix, that's the mentality they have," Wane told Sky Sports News.
"I told them the way we played wasn't us, that we needed to sort our defence out. I admire the players so much, the character and the tough men that they are.
"I was expecting a few apologies after how we have been doubted this year. The players got hammered. I can't tell you how proud I am."
The last team to do the double was Wigan's arch rivals St Helens in 2006.