Reguler screw will not hold.
More info is needed. Tap Con screws are avalible in at least 4 differant sizes and will work fine with any threshold I've ever worked on.
Tap Cons are screws not bolts. Are you using flat head Tap Cons?

 

Ditto on using flat head Tapcon screws.
http://www.concretescrews.com/
The screw head can be counter bored ¼” and covered with a plug.

For installing a ¾” thick threshold a common Tapcon length is 1-3/4” or 2-1/4”.

Caution on using an extra long screw. They will break, I’ve done it.
Tapcon says the screw embedment s/b a minimum of 1”, maximum of 1-3/4”

 

Is this an exterior threshold?

If interior---use PL premium---drilling holes into the concrete and pounding in wood dowels will allow you to use regular wood screws---but I would not use that for an exterior install--water will eventually soften the wood plugs.

 

I thought those blue bolts were Tap con. I better double check. I always tightened them down with a small crescent wrench.

 

Yes sounds like they are, however there are different kinds, have a look to find ones that will set flush with the threshold.

 

I got some tap cons in screw configuration. Thanks guys.

 

what kind of threshold is it? wood/metal?

 

metal