Powell, who replaced Ian Millward last month, masterminded one of the shocks of the season as the Tigers took advantage of an injury-riddled Warriors outfit to claim an 18-4 win.
When asked if Cas, who are currently five points behind eighth-placed St Helens, could reach the play-offs, he said: "It's possible. It's a really tough challenge but I sort of set things out when I got to the club. We broke it down into blocks and we needed to do certain things which we didn't do in the first block."
He added: "I think being able to perform like we have done has given us a little bit of belief that there is a chance. It's still a tough one but you have to believe in achieving something special and I think we do believe that at the moment."
The former Leeds boss also admitted it was the best team performance he had witnessed since taking over in May.
"Defensively to concede four points against any Wigan team is a massive effort so I was delighted with the overall performance," he added
"The spirit and toughness of the side is growing all the time and I'm really delighted. Some of the tries we scored were fantastic and we are growing as a team all the time. The commitment and effort is first rate."
Wigan coach Shaun Wane refused to blame Monday's night's bruising encounter against Warrington for the loss as the Warriors fell to back-to-back defeats.
"It was a poor performance," he said. "I thought Castleford were really good, they defended well and they handled the conditions better than us. I want to commend them because Daryl has done a great job while he has been there and the best team won.
"No excuses (from Monday), I still expect us to perform. For me to say that would take something away from Castleford and I thought they were good and the best team we have had here. We lacked a bit of energy and if that is because of last Monday then I expect us to get over that. We are better than that and it will never be used as an excuse."