Saints ran in three tries in each half to take advantage of a weakened Wolves pack and put a dampener on their hosts' 10th stadium anniversary celebrations.
"Warrington as a team have been so successful for so long so to get the result was pleasing," Brown said.
"We're really rapped with what the guys did but we're certainly not going to get carried away.
"It's a good start but it's about consistently doing well."
Saints' match-winner was Australian scrum-half Luke Walsh, who scored a try and kicked seven goals from as many attempts on his Super League debut, while fellow newcomer Kyle Amor was also a tryscorer.
"Walshy had a lot of good contributions for us, built on the back of some of the forwards' work," Brown said.
"I thought our game management in the second half was actually quite poor but it's clear to see what Walshy can bring to the team."
Brown was also delighted with the contribution of Walsh's half-back partner Gary Wheeler, who has struggled through injury over the years to break into the Saints first team.
Wheeler got the nod ahead of former New Zealand international Lance Hohaia and Jordan Turner, who reverted to centre and carved out a try for winger Tom Makinson.
"We trained with lots of people at six in pre-season," Brown added. "Wheels had a nasty injury last year and he was still in rehab for a period of time early in the pre-season.
"But he's trained the best he's ever trained to put himself in position and I think everyone would agree a fit Gary Wheeler is a terrific young player.
"Hopefully his body can hold up but we know we've got Lance there.
"It breaks my heart not playing Lance because he deserves to play every week. He's a terrific player and a great bloke and it's not nice to leave him out but I can't find a spot for everyone."
Warrington, Grand Final runners-up for the last two years, began life without departed former captains Lee Briers and Adrian Morley and with three other forwards sidelined through injury.
They made a dream start with winger Joel Monaghan opening the scoring in the second minute with the first of his two tries but coach Tony Smith admitted his side were well below their best.
"Our kicking game was right up there with one of the worst we've had for a while," he said. "We got out-kicked, that's for sure, and around the ruck area we weren't great.
"I thought in the first half both teams competed pretty well and there was not much between us. They were good when they had the ball and we troubled them when we had the ball.
"In the second half they were way better than us. There was too much panic from us. We were chasing the game instead of having patience. It was a bit of a kick in the backside for us.
"I thought Saints were terrific. They got on a roll and did all the little things well."
- Sports & Recreation