The South Yorkshire metro mayor ripped into the company after new timetables and services resulted in a lack of drivers, cancelled services and furious commuters across the north of England.
Mr Jarvis, who commutes from Barnsley into Sheffield as mayor, said he has experience the problems first hand and said the service at present 'should've been consigned to the past'.
Northern rail bosses have said they're 'truly sorry' and Transport Secretary Chris Grayling in a letter to MPs also hit out at the service.
Mr Jarvis said: "I'm not the only one but I'm incredibly concerned about performance of Northern rail in recent times.
"The existing service going to and from Sheffield and Barnsley for example it's just not good enough at the moment.
"Both as mayor and as a commuter - I absolutely share those concerns and frustrations - I experience them on a daily basis myself.
"It's like going back in time and not in a good way using that service. It feels like a service that should've been consigned to the past. People deserve a better, more modern service
"It simply isn't good enough - whilst people can accept delays occasionally for reasons out of their control - essentially at the moment we don't have a system that's fit for purpose in 2018."
Mr Jarvis said he will be meeting with Secretary of State Chris Grayling on Thursday to see what national Government can be doing to improve the service.
The mayor added he was writing to Northern this week to air his concerns about the chaotic service.
In a letter published on Wednesday, Transport Secretary Chris Grayling said in a letter to the Yorkshire MPs that the level of disruption on Northern rail last week was 'wholly unsatisfactory' and the scale of the chaos 'far outstripped any expectation'.
David Brown, managing director of Northern, said: “Our plans for modernisation are not all being delivered in the way we want. We are doing everything we can to minimise cancellations and delays and keep our customers informed.
"It has been difficult for many of our customers and I am truly sorry for this. There is urgent work to do to fully understand what did and didn’t work on all aspects of planning and delivery of the new timetable.
“We are committed to working with Network Rail to get things back on track as quickly as possible, and to deliver the services our customers expect and deserve.”