very sorry in English:

‘Sorry,’ she said, with an apologetic smile.

She was so apologetic about forgetting my birthday it was almost embarrassing.

He was most apologetic about (bardzo przepraszał za) his son’s bad behaviour.

Audrey was extremely apologetic for having kept us waiting so long

The manager was very apologetic about everything.

He was very apologetic

an apologetic smile

He was apologetic for being absent.