Ireland Under-20s head coach Murphy is in charge until the end of the season after replacing Dan McFarland, who left his role in February.
Ulster have only won one of their four matches under Murphy and face Cardiff in Belfast on Friday.
“How confident am I? I’m very confident and I’m very confident in the team as well,” Murphy told BBC Sport NI.
I’m confident in my own ability as a coach to help point teams in the right direction and drive the standards that are needed in order to be able to play at the very top level.
Murphy’s tenure started with defeats by Sharks and Stormers in South Africa, before a big win away to Montpellier in the European Challenge Cup was swiftly followed by a heavy defeat quarter-final loss to Clermont Auvergne.
His first home fixture will be at home to Cardiff on Friday, and Murphy, who has previously said he would like to stay on beyond this season, says he has “really enjoyed” his experience in Belfast to date.
“I’m definitely enjoying the job. I’m frustrated sometimes, delighted other times – all of the emotions that come with professional rugby,” said the 49-year-old, who added he was “blown away” by the opportunity.
“Over the past couple of weeks it has been tough and intense, but I’ve really enjoyed it.”