Although having the majority of possession Arsenal failed to extend their lead with the Baggies having chances to equal the scores with Kim Do-Heon, Ishmael Miller and Paul Robinson all coming close.
"In preparation for games like this you run through all the scenarios in your head," Tony Mowbray said.
"One of those scenarios is getting a good hiding and when they scored after four minutes that was always going to be a possibility.
"It was a stereotypical first day of the season.
"It was hot out there and there was an opening day feel to it.
"The fans were in buoyant mood, Arsenal were moving the ball around and we could have been in trouble.
"But we stuck to our task and worked extremely hard all over the pitch.
"The longer the game went on the more of a threat we looked in terms of scoring a goal.
"If it wasn't for a decent save by their keeper, and a clearance off the line, it might have been 1-1.
"You don't get any points for losing 1-0 - but that's football.
"We came with a gameplan and Arsenal are what they are.
"They're a slick, fast-moving, football team.
"Regardless of who is in their team, they seem to play the same way and we had to stick to our task.
"I thought we did that."
Mowbray, like many Albion fans, took positive from the nature of the defeat, and although Albion are yet to register any points, took lots of heart from the performance ahead of the Everton game.
"I'd be a lot happier if we were sat talking about a 1-1 draw but I have total respect for Arsenal," Mowbray continued.
"They had numerous opportunities and a number of things that went close.
"Every team that comes here will suffer that - Arsenal do create chances.
"To come away feeling as if we might have sneaked something means there are positives to take from the game.
"We've earned the right to be in this league and we aim to make sure we stay here.
"Today was day one and we've got another 37 to go.
"We'll be competitive in every match and I thought we were competitive today in the context it was Arsenal we were playing.
"I'm very, very confident we won't be written about, as the season goes on, as 'little old