Fer Lopez’s goal was the difference, but in reality Wolves dominated the game and should have scored more against a lacklustre Baggies side.
The Molineux atmosphere was intense and loud throughout and Peixoto was delighted with the backing, performance and result - but is keen to stay grounded ahead of a long season.
He said: “The fans today are amazing. I think the team pushed them to support us until the end because the team did a great job today.
“This win is important for the supporters, but it’s only three points in the pocket for us.
“The Championship is too long, too tough and we have to stay with our feet on the floor and work hard like we worked here.”
Peixoto added: “It’s very important.
“It’s only three points, we know the importance this game has for our supporters. We want to win this game for our supporters, but for ourselves also.
“I think the players deserve this win. They play during 90 minutes with a big soul, big organisation, big quality. We created a lot of chances. We can score more goals, but it's an important win.
“We’re going to rest now because of the national teams, it’s an important rest with a win and to come back as strong as possible when we return to training.”
Wolves now head into a long international break without a game until October 10 when they travel to face Middlesbrough.
Peixoto said.“It’s important we win. We played four games away. We return to our home, a derby, an important game for our supporters. Good team, West Brom, they have more points than us.
“It’s a very important victory because of that also. The way the players played, I like the way we play. When we have to press high, we press high.
“We react stronger. We play with quality. When we have to, in the last minutes, suffer a little, we close the team.
“We deserve it. We can score more goals, but we deserve the win. This kind of environment, the way the team played today, made me happy, for sure.”
Meanwhile, Ladislav Krejci was unavailable for the game due to a calf injury.
Peixoto implied in his press conference that Krejci ruled himself out of the game, in order not to worsen his injury ahead of the international break.
Czechia play four matches, including against England at Wembley in October.
“He felt a little thing and he didn’t want to take risks,” Peixoto said.
“We play with the players who want to stay 100 per cent with the team, with the club. “We fight until the end to win this game in a good way. We played well.
“For me, the most important thing is the team, not the player A, B or C. We stay together. We stay organised. We play with quality.
“The players are all important, but I believe in all the players. For me, it’s clear.”
When asked if Krejci will be available after the international break, Peixoto added: “I don’t know what’s going to happen, if he goes to the national team.
“I think when he comes back, he’s our player. I hope he stays well to train and play.”
Not sure how to take the Krejci thing. If he's injured fine, but that reads like he's sacrificed this match for the internationals... Which if he has, he needs to go in Jan. That's not what you want in your team
Hes captain of his country....quite a big honour to captain your country i would suggest so maybe thats the reason he didn't want to risk injury being worse.....not trying to make excuses for him but just trying to understand the situation