Under my employment contract, I am entitled to 11 statutory holidays.

This year ANZAC day fell on a Sunday, which is not a day I usually work.

I believe that I am entitled to a paid day off in lieu because otherwise I would not receive my full entitlement of 11 statutory holidays. But, my employer disagrees.

Is my employer correct?

The answer to your question depends on the precise wording of your employment contract. The wording is likely to be the same as, or similar to, that found in the Holidays Act 1991.

If so, then you are only entitled to a paid day off if ANZAC Day (or any other statutory holiday for that matter) fell on a day you would otherwise have worked. As ANZAC day fell on your normal day off, you are not entitled to payment for it.