apologetic
apol·o·get·ic
/əˌpɑːləˈʤɛtık/ adj [more ~; most ~]
: feeling or showing regret : expressing an apology
We received an apologetic letter and a full refund from the company.
an apologetic smile
They were apologetic about the mistake.
She seemed almost apologetic about buying a new car.
apol·o·get·i·cal·ly /əˌpɑːləˈʤɛtıkli/ adv
He smiled apologetically.
“I'm sorry I'm late,” she said apologetically.