Moors remain at the foot of the Vanarama National League despite winning beating the Spitfires - watch match highlights here.
Jermaine Hylton put Richard Money's side ahead after just four minutes and then Oladapo Afolayan added another in the second half.
Ben Williamson quickly pulled one back for the hosts but it wasn't enough as Eastleigh remain in 17th.
The performance left boss Hill seething, he said: "It wasn't good enough. We had two good chances in the first five minutes and we didn't hit the target. After that it just wasn't good enough. It's a bit embarrassing to be perfectly honest with you.
"We had spell 10/15 minutes in the second half where we huffed and puffed and flattered to deceive a little bit.
"It's embarrassing, again I'm having to come and apologise to people. I suppose there'll be a few out there who have a bit of fun saying it weren't even value for money for being free, but it probably wasn't, was it?
"I'm the manager, I take the blame but I actually didn't head it to their player. As silly as it sounds, I didn't head it to their player for them to score but I'll get the blame for that.
"It just wasn't good enough, it wasn't acceptable. The lads are in there and I think they're a little embarrassed themselves if truth be known."
Picture: Graham Scambler
For more coverage, reaction and some of the best moments from games going throughout the season, head to our social media channels on Twitter, Facebook and now Instagram.