Staff were assaulted on four occasions, with one worker hospitalised; people exposed themselves to staff and there was a stabbing outside the premises. One of the assaults took place at 10am.
The owners say it was a choice between closing or hiring security.
"Temple Bar was not the right spot. We need a place that feels safe and happy and fun and in Temple Bar you get that sinister element that turns up once in a while," Sean said.
"There would be individuals who would turn up and they would not be regular people with a bit too much drink on them. They're on much harder stuff. They're troublemakers," he said.
But he insisted the experience did not put them off Dublin and that, while Temple Bar was not right for them, it was a great place for many other businesses.
Murphy's opened in Wicklow Street and in Temple Bar in 2010.
While the Wicklow Street store is thriving, "there were a few tough individuals who would turn up [in Temple Bar] and you'd never know when they would turn up," Sean said.
When people think of the area, they tend to think about groups on a night out, but there is "another part of Temple Bar", he added.
"But the fact of the matter is that Dublin has been really good to us."
David Brennan, the chief executive of the Dublin City Business Association (DCBA), said it had been raising the issue of antisocial behaviour in the city centre for a long time.
He linked the problem to the number of drug treatment centres located in Dublin 1.
"We as an organisation have been looking at this for years but nobody has bothered to listen to us," he said.
"We have seven treatment centres in Dublin 1," Mr Brennan pointed out. He said this was unreasonable and unfair.
"I think the treatment centres should be moved out of the city centre. We're the only country that I'm aware of that would have a cluster of centres," he said.
"We're getting it from the tourism side.
"Our tourism figures are diabolical. I believe antisocial behaviour has something to do with it," Mr Brennan added.