FRANKFURT, May 16 (Reuters) - Big investors in Deutsche Bank vented their frustration at Germany's top lender on Thursday, describing problems at its Postbank business as a trust-damaging embarrassment.

The complaints at Deutsche's annual general meeting follow the bank's disclosure that a long-running lawsuit claiming that it underpaid for its purchase of Postbank could cost up to 1.3 billion euros ($1.4 billion).

Andreas Thomae of Deka Investment addressed Deutsche Bank CEO Christian Sewing directly, saying: "This news hit us like a thunderbolt. It has once again destroyed trust, which Deutsche Bank cannot afford."

Though Deutsche recently presented better than expected earnings, it has struggled for years to integrate Postbank fully. Soon after saying it had completed the technology integration, glitches locked customers out of their accounts for weeks.

"The problems with Postbank's IT migration are an embarrassment. A bank should not leave its customers in the lurch like Postbank did," said Alexandra Annecke, fund manager with Union Investment.

She said the matter raised questions about whether Deutsche Bank would be able to handle merger and acquisition opportunities that could arise.

CEO Sewing told shareholders the bank was sorry for the glitches and that Deutsche had fallen short of expectations.

The provisions will have a negative impact on results but does not change the company's strategy, he added. ($1 = 0.9200 euros) (Reporting by Tom Sims Editing by David Goodman)