And it is about more than the type of profit on the balance sheet their debut campaign brought in last season.
Albion showed a £20 million profit on a Europa League adventure with saw them top their group and play eight games in total, winning five.
Barber described that income as “hugely valuable”.
It contributed to a profit of £73.9 million last season.
But the club – led by chairman Tony Bloom – see European status as worth more than the obvious income and are keen to get back inro that sort of company.
It could happen as soon as next season as they remain well-placed in the league and still alive in the FA Cup.
Barber, the cub’s chief executive and deputy chairman said: “It is interesting now.
“Whenever we go to football events, and this is anecdotal and a small point in some ways, even this week at the Financial Times business of football summit, the number of European club chief executives who came up and wanted to talk because they knew who we are.
“They had seen us in European competition.
“They had seen us at the draws in Monaco and Switzerland.
“Just one season in Europe and doing relatively well in our first season has elevated the club’s profile among European football clubs.
“Of course, our reputation in the Premier League and with player trading has all helped but being in European competition does more for the club than just bring in £20 million worth of additional value.
“It elevates our club to a different level of football society, if you like.
“Why does that matter? It matters because, when we look to bring in players, our profile is that much higher.
“They are aware of us, they are aware of what we are doing.
“It matters because sponsors are looking at us in a different way and looking to make sure they are working with clubs they see as being aspirational and inspirational.
“It helps us in so many different ways that are very hard to quantify directly but are so valuable to the journey we are on and building the club’s profile over time.
“It is something that in 13 years I have been here – and before me when the club moved to the Amex – establishing the club as part of the football world at a higher level was a really big ambition of Tony’s.
“This was a club that for over a century had largely moved between the bottom two divisions.
“Tony’s ambition in bringing the club here was we would be working at the highest level and be established at that level and work hard to even improve at that level.
“That is the journey we have been on and are still on and will be on for some time.
“We have said many times we are still relative novices in the Premier League so we are certainly novices in European football – significant novices.
“To be able to go into a second season of European football would be fantastic.”
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