FRANKFURT, June 6 (Reuters) - A few conservative European Central Bank policymaker expressed regret on Thursday about signalling too explicitly that a rate cut was coming and some even said they might have otherwise voted for holding rates, four sources told Reuters.

The ECB cut rates from a record high on Thursday given a decline in inflation and only Austrian central bank chief Robert Holzmann objected, giving the decision broad-based support.

The move was well telegraphed after most policymakers in the lead-up to the meeting backed the cut and Vice President Luis de Guindos even called it a fait accompli.

However, a string of worrisome wage and price data in the final weeks before the meeting altered the outlook and raised doubts about the ECB's narrative that inflation was heading back to target by mid-2025 with just a few bumps along the way.

An ECB spokesperson declined to comment.

The sources, all with direct knowledge of the discussion, said that around a half dozen conservatives noted that this recent run of data may not be consistent with a rate cut, so the move was more a judgment.

A smaller number even said that their final decision might have been different without the pre-commitment.

But other than Holzmann, all agreed that backing out of the commitment would be a mistake and deeply divisive.

Still, they made the case that the ECB needed to live up to its commitment to basing decisions on incoming information.

Speaking after the meeting ECB President Christine Lagarde also struck a cautious tone and gave almost no hints about the ECB's next move. (Reporting by Balazs Koranyi and Francesco Canepa; editing by Mark John.)