Emas responded to 71.6% of Red 1 calls and 70.2% of Red 2 calls in 2014/15 - missing the 75% target.
Red 1 calls involve life-threatening injuries, while Red 2 calls include serious breathing difficulties.
Emas chief executive Sue Noyes said the service was improving and had hit the 75% target in April and May.
It also missed a target of reaching 95% of both Red 1 and Red 2 calls in 19 minutes by 2.2%.
Ms Noyes said calls to the service were up by 22%, almost 200 more each day, in December and January.
"The figures that we've had for last year reflect the fact that we had that extraordinary winter in terms of demand," she said.
"What we did see last year was that we did deliver all three targets for the first quarter of the year; now that was the first time we've delivered that in five years," she said.
She said the service was mid-table in a list of national ambulance target figures, which are due to be released by the Department of Health on Wednesday.
Emas said it was recruiting 200 extra frontline staff, and investing Â£3.9m in new ambulances.
The ambulance service covers Derbyshire, Leicestershire, Rutland, Lincolnshire, Northamptonshire and Nottinghamshire, and handled more than 643,115 emergency calls in 2014/15.
East Midlands Ambulance Service (Emas) has failed to hit targets to reach the highest priority calls for a fifth year running.