The operator, which runs several lines across the North, said it was "truly sorry" for the disruption caused by the introduction of new timetables last week.
Northern, in a joint statement with Network Rail and Govia Thameslink (GTR), which has also seen delays and cancellations, said "comprehensive plans" to reduce disruption were being worked on "urgently".
But they warned: "Unfortunately, it will take some time to deliver significant improvements to services, but we will keep passengers up to date on all changes we make."
Affected passengers have been encouraged to apply for "delay repay" compensation, and the operators promised they were "working hard to respond to all claims as soon possible".
Northern managing director David Brown added: “We are doing everything we can to minimise cancellations and keep customers informed. It has been extremely difficult for many of our customers, in particular on a number of routes around north Manchester, Liverpool, and Blackpool extending up to Cumbria, and we are truly sorry for this.
“We‘ve agreed a number of actions with the Department for Transport and are urgently working with them on a comprehensive plan to stabilise our services. Such a plan is likely to take a number of weeks to deliver lasting improvements, but we recognise our customers deserve better and that’s what we’re focused on.”
The joint statement said the timetable changes introduced on Sunday May 20 were "the most ambitious in recent railway history" and were designed to provide additional capacity for tens of thousands of commuters.
Each of the new journeys had to be approved by Network Rail, the state-funded infrastructure operator.
But the "sheer number" of timetable changes and the late running of engineering works, such as the electrification of the line between Bolton and Preston, for which Network Rail is responsible, meant "the process took longer than anticipated, approvals for service changes were delayed and some timetable requests were changed".
"Whilst circumstances differ across the country, this meant that train companies had much less time to prepare for the new timetable which required trains and drivers to run on different routes," the operators said.
"The differences between the timetables submitted and those approved created a requirement for training that had not been anticipated. This meant that the necessary specialist training was not able to be completed in time for drivers to learn new routes and for operators to address all the logistical challenges.
"The operators are now reviewing how timetable changes are introduced to ensure the chaos suffered by passengers in recent days is no repeated.
Mark Carne, Network Rail’s chief executive said: “There is no doubt that the May timetable was finalised significantly later than normal for reasons that were both within and without our control. The consequences of that have been particularly hard for both Northern and GTR to absorb.
"But we are all firmly focused on fixing this issue as quickly as possible to give passengers the reliable service they need and deserve. At the moment, in some parts of the country, that simply isn’t happening and for that I’d like to wholeheartedly apologise.”
Charles Horton, CEO, GTR, said: “We always said that delivering the biggest timetable change in generations would be challenging – but we are sorry that we have not been able to deliver the service that passengers expect.
"Delayed approval of the timetable led to an unexpected need to substantially adjust our plans and resources.
"We fully understand that passengers want more certainty and are working very hard to bring greater consistency to the timetable as soon as possible. We will also be working with industry colleagues to establish a timetable that will progressively deliver improvement.”
Transport Secretary Chris Grayling was yesterday accused of "passing the buck" for failing to apologise in a letter to MPs whose constituents have been affected by the chaos.