A 28-18 success at the Jungle lifted Tigers above next week’s Ladbrokes Challenge Cup finalists into third place on the table.
Tigers led 16-0 at half-time, but Warrington replied with two converted tries at the start of the second half before the hosts regained control late on.
Powell said: “I thought we were good for large parts.
“I thought we were controlled in the first half, but at the start to the second half we didn’t come out of the changing rooms that well.
“We conceded a couple of tries from kicks; the first one in particular I don’t know how you defend that. You just have to invent another player to turn up - it was a perfectly executed kick.
“In general, though, it was a big win. There was a bit of nervousness because had we lost [the week before] and Huddersfield are sneaking up and have a lot of momentum.
“It eases the pressure and gives a chance to have a little bit of a breather.
“We have another home game then against Catalans so it is set-up to start and develop some consistency about us.
“Hopefully, as well, we will have some more competition for places which hasn’t been there for some weeks.”
Peter Mata’utia, a recent signing from Leigh, made his home debut and became the seventh player used at full-back by Tigers this year.
“I thought he was excellent,” Powell said.
“He was really solid. His high ball stuff is great, he carries the ball well, he has clever bits about him.
“It will take him time to piece everything together, but he is really diligent, he studies the game closely and watches everything we do over and over again. He is going to be a great signing.
“We have played a lot of people at full-back trying to sort the equation, but he was really good. He has got the full package.”
Greg Eden scored two of Tigers’ five tries, but Powell wasn’t entirely happy with the winger who almost lost possession diving over for his opening score and put a foot in touch when he had an opportunity later in the game
“I don’t know what he was doing with the first try; I don’t think he needed to do that,” Powell said.
“I think he needs to do a bit better at staying on the field - it’s a pretty important part of the game.
“Some of his decision making needed to be better but they were important tries.”