NR was expected to run 92.5% of trains on time in the five years to the end of March 2014, but the company only reached a figure of around 90%.
This means it could face a fine from the Office of Rail Regulation of up to £70 million, although the five-year period has included heavy snow, severe storms and floods.
NR's punctuality target for 2014 to 2019 is also 92.5%.
An NR spokeswoman said: "Missing our regulatory targets for punctuality is disappointing and our focus for the coming five-year period is to restore record levels of performance and spend and invest some £38 billion in our railways targeting the busiest parts of our network to relieve congestion and provide more trains, more seats and quicker, greener journeys."
Transport Secretary Patrick McLoughlin said: "A key part of this Government's long-term economic plan is investing in world-class infrastructure. That is why we are putting record amounts of Government funding into our railways over the next five years.
"That investment will generate growth, create jobs and boost business while delivering faster journeys, greater comfort and better punctuality for passengers across the UK."
Meanwhile, NR's new chief executive, Mark Carne, hinted in The Independent today that pay for senior staff would be reined in following an outcry over bonuses at the company.
Mr Carne said he would take executive pay proposals to NR's annual meeting in July, adding "We need to ensure that we hire good people who are well paid, not overpaid."
NR also announced today that the storm-wrecked railway line at Dawlish in Devon will reopen as planned at the end of this week.
The coast-hugging stretch of line was first severely damaged in the saveage winter storms and then damaged again in another violent storm on February 14.
With the line shut and round-the-clock work going on to bring it back into service, a massive landslip, involving the collapse of 20,000 tonnes of cliff-face near Teignmouth on March 4, had threatened the planned reopening.
But NR said today that the reopening - on Friday - was going ahead.
Mr Carne said: "Dawlish has shown us at our best when we work in a planned, disciplined and innovative way.
"Our aim is to emulate that approach and embed it in our organisation so that we are continuously improving the service for our customers."