In a note to clients issued Tuesday, Barclays Capital’s Ben Reitzes has added his voice to the chorus of commentators with free advice for Apple’s (AAPL) executive team, now that it’s caught the eye of federal regulators.

The Federal Trade Commission has reportedly won the toss and is looking into two possible antitrust issues: Adobe’s (ADBE) complaint that Apple doesn’t allow Flash on its mobile devices and Google’s (GOOG) complaint that Apple restricts AdMob’s ability to sell ads within iPhone and iPad apps. Meanwhile, the Department of Justice is still seeking information about Apple’s role in the music business, which could lead to a separate antitrust case.

Reitzes, like most commentators, believes Apple’s less-than-dominant share of the smartphone market should give the company ample defense — “for now.”

But he also thinks the company needs an attitude adjustment.

“We are watching these developments carefully,” he writes, “and believe that Apple has to be more careful about how its comments and actions are portrayed – rightly or wrongly by regulators – now that it is the largest tech company by market cap in the world. Apple still seems to have an “underdog” attitude and it was only a few years ago that investors were calling for it to adopt the strategies of tech laggards like Microsoft and Dell. While the underdog attitude keeps the company driving for growth and over-achieving – we believe the world no longer thinks of the company as an underdog at all.”

He notes that although Apple dominates the market for music and mobile apps, its share of the global cellphone market is less than 2% and it still has only a 15% share of the smartphone market.

“We believe Apple has a lot of things going in its favour,” he concludes, “and we would be surprised if regulators could slow them down over the next 2-3 years.”

[Follow Philip Elmer-DeWitt on Twitter @philiped]