Two second-half goals from JJ O’Donnell were the difference as the Reds began with a loss after what had been an encouraging pre-season.
And Heath was left to lament his side’s second-half display in particular.
He said: “We had a good 20-minute spell in the first-half where we had a couple of really good chances and didn’t take them.
"On the opening day of the season an early goal can settle you down and gives you more confidence than you’ve already gained – we really should have taken one of them.
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"We started off the game pretty well and had those chances but then I was disappointed with the second-half as we never reached the heights of what we’d achieved in pre-season momentum-wise and with our play.
"The two goals were really disappointing and really cheap to concede as we just didn’t deal with things.
"In this league, if you’re going to be naive you’re going to get punished.
"We came in at half-time at 0-0 and a point away from home would have been a good result at a difficult place to come, but in the second-half I don’t think we showed anything like what we’re about and I thought we were quite poor.”
Hopes were raised in the opening 15 minutes with a series of attacks by the Reds which yielded only one direct shot on target when Dayle Southwell tested home keeper Alex Mitchell with a fourth minute angled drive.
Bobby Johnson then pounced on a loose ball but fired hastily over when well placed.
Josh Clackstone was forced to clear off the line from Blyth’s Dan Maguire, then Johnson squared a freekick to Rob Evans but the midfielder could only skew the ball on to the roof of the net.
Blyth started the second half the stronger with Robbie Dale missing a great chance before O’Donnell then tucked a Thomson cross from the left out of the reach of George Willis.
On 56 minutes Willis pulled off a great save from Thomson at the expense of a corner from a Dale through-ball, then at the other end Johnson’s shot was blocked.
O’Donnell doubled Blyth`s advantage with 65 minutes on the clock, finding the corner of the net from a left wing cross.
Alfreton could only muster openings from Johnson, whose shot failed to trouble the keeper, and Elliott Reeves whose shot was deflected into Mitchell’s hands.
Alfreton now prepare to host Brackley Town at the Impact Arena on Saturday, with original opponents Leamington unable to play having also seen their opening game with Gateshead postponed last weekend due to positive COVID-19 tests.
Heath added: “Every game is huge. We’ve started the season and needed to get something at Blyth but we’ve got to now make sure we get things right against Leamington and answer more questions people pose us.
"We definitely have to step up to the plate on Saturday.”