Ok, let's just be clear on the mathematics of this. The Milky Way is anywhere from 100,000 to 120,000 light years across, depending on your starting point. That means as a if you can travel 10LY per day it would take you 27.4 to 32.9 years to travel from one end of the galaxy to another, provided you never have to stop.
However, in the ME universe you do have to stop. There are four reasons you need to stop:
1. Discharging your drive core. This needs to be done somewhat frequently.
2. Get more food supplies. Other than the quarians, none of the races really have ships built for growing food for long term travel. This means that along the way you need to find garden worlds that have suitable foodstuffs, which given the relative rarity of garden worlds and the fact that not all garden worlds have food that is good for every species, this is a very risky proposition. You're quite likely to starve on any truly long term trip.
3. Fuel. The Normandy can run out of fuel just by traveling withing a single star cluster and not refueling. Unless you either have the infrastructure to extract the necessary elements for fuel on your ship (again, like the quarians would) you're not going to get far. Given that the Reapers have destroyed many fueling stations and a lot of infrastructure used to make fuel, this is going to be a problem. It's even further a problem because the further you get from a relay, the less likely that infrastructure is going to exist at all since galactic civilization centers around the relays.
4. Maintenance. Your ship is going to break down. Parts aren't usually just laying around. EDI mentions in the game that the Normandy will need maintenance before the year was out, and the damn ship was just refit before the game started. Imagine a decade or more long journey where you have to do the maintenance without a facility to do it in. The quarians had this problem with the Migrant Fleet, and they were able to make their own parts when needed.
Basically only the quarians would be prepared for any truly long distance travel, while the rest of the galaxy isn't remotely prepared for that. They are stuck in their local areas, and many remote colonies are cut off from the resources they'd normally use to grow.
(The Reapers probably got around 1, 3, and 4 through more advanced technologies, and had no need for 2)
Even if they can build new Mass Relays, that will take decades if not centuries as they are massive structures that require very large amounts of element zero.
The Earth equivalent would probably be if we lost the technology to make planes, cars, and powered ships and had to travel by horse and sailboats again. Yeah we could reach one another in time, but the resources for the trip would make it hard to be worth it.