Mr Hirst said the system was introduced because anglers requested it.
But Greenstone Fishing owner Dave Bedford said the digital process was an unwanted burden and he was forced to hire another staff member over the holiday period to deal with licences.
He said there had been no consultation before the change.
"I'm a one man operator, and Boxing Day I had to employ someone just for the licences. I could have done with that person several times over the past few weeks but it costs too much.
"I takes a good five minutes at least to process each person, before I could hand over the licence book get them to fill it out and I could serve a customer. But I've had people walk out of the store because I was tied up doing this."
He added: "As far as I'm concerned it's easy for a Government department to implement these things and then go off on a three-week holiday and be unaccountable.
"It's terrible timing, it's one of the busiest times of the year and to top it off an awful lot of businesses like the corner dairies, have chosen not to be online retailers so that's put extra pressure on the tackle stores."
Taupo fishing guide Brent Pirie said his international clients were having to face a lengthy wait before they could go on the water.
"It ties us up, I had the other day a mum, dad and two children and it took up to 25-30 minutes. Each transaction has to be processed individually, you can't just buy four licences and pay with a credit card at the end," Mr Pirie said.
"Why couldn't they have done this in the middle of winter when we don't have all the international visitors? I know for retailers it has really impacted on their sale times."
Mr Pirie questioned whether the licence was legal when an angler wasn't able to sign the document because there was no nearby printer.
The department apologised for some delays people may have faced.
"If people have purchased a fishing licence online and haven't been able to print their licence they can use the digital copy of the licence they received by email as proof that they have a licence," Mr Hirst said.
"We know that some people have been taking photos of their digital license and the Department of Conservation is happy to accept this as proof that they have purchased a licence."