By Svea Herbst-Bayliss and Tim McLaughlin

NEW YORK (Reuters) - Embattled BNY Mellon Corp <BK.N> CEO Gerald Hassell, under fire from activist investors, received a public rebuke on Tuesday at the bank's annual meeting for lagging past performance, but also a vote of support to make improvements going forward.

The words of criticism and support came from Ed Garden, who joined BNY Mellon's board in December. Garden is a senior executive at Trian Fund Management LP, the activist hedge fund run by billionaire Nelson Peltz that owns about 2.6 percent of BNY Mellon's stock.

"Nobody is satisfied with past performance," Garden said toward the end of the hour-long annual meeting in New York City. But at the same time, Garden said the bank's board supports Hassell and his management team, though they will be held accountable for meeting the financial targets they've laid out.

Hassell, who became CEO in 2011, has been criticized by investors and analysts for missing key targets, such as profit forecasts. Earlier this month, activist hedge fund Marcato Capital Management said BNY Mellon's employee base is "bloated" and disproportionately larger than its rivals. Marcato said the bank has 10,000 excess employees.

"We know there are things we have to do better," Hassell said.

About 40 people, not including board members and senior executives, attended the annual meeting, which also was webcast.

Annual meetings tended to be scripted events, but Hassell patiently fielded several pointed questions from outspoken banking analyst Mike Mayo of CLSA.

Mayo, for example, asked Hassell why it has taken so long to reduce the number of custody platforms at the world's largest custody bank. Hassell said the bank now has two custody platforms, down from four, and he expects to only have one by this time next year.

Mayo also asked why the bank has lost market share in its core custody business.

"It's slipped a little bit. I'll admit to that," Hassell said. But he added the bank has been more selective in adding clients, to ensure the business is profitable.

Hassell has made a number of moves to streamline the bank's operations, such as selling its headquarters and its corporate trust units in Japan and Mexico.

Garden joined Hassell in offering an upbeat outlook for the bank.

"We're going to be a force to be reckoned with in everything we do," Garden said.

(Reporting By Tim McLaughlin and Svea Herbst; Editing by Chizu Nomiyama and W Simon)