Every airline has its own rules about what routings they will sell and allow, and Delta's are likely more restrictive than Virgin's since Delta has more hubs and routings they can put you on, so they will suppress some more out-of-the-way routings like this one.

Are you looking at cash or mileage tickets? If cash tickets, you could try calling Delta and see if they will sell it to you, though it's possible they won't or it may be more expensive than Virgin -- or you could buy from Virgin (with some possible impacts in terms of mileage and MQD earning and upgrade potential).

If mileage, it doesn't really matter what you found with Virgin because Delta doesn't have "standard" awards any more so if you wanted to use SkyMiles instead you'd be at the liberty of whatever Delta wanted to charge in mileage, which may be very high (though note that Virgin Atlantic miles can be obtained by transfer from various credit card programs like Amex Membership Rewards and Chase Ultimate Rewards, and note that Virgin often charges high cash co-pays on awards).