Will cement used as mortar need to be replaced?
It depends... 

These days, bricks are used far less frequently as the "structure" of residential homes, due to the higher chance of failure from lateral movement (such as an earthquake). Depending on the construction of your home, they may provide little to no structural value and may be purely cosmetic.  If they are cosmetic, the structure should not be compromised any more than it was when the mortar failed (which would typically mean "insignificant"). If they are structural, your concerns may be warranted.

If your house was built more recently, uses primarily wood framing including along the interior sides of your exterior walls, and your rafters/trusses are fastened to said framing (rather than fastened to the bricks), it is more likely to be cosmetic. It is extremely telling in the case where the brick stops before it reaches your roofing timbers. That is not to say the brick provides absolutely no structural value -- it still serves a purpose and can help resist movement, but cosmetic brick does not bear the structural loads. If you've seen a home built with brick recently, you likely saw a free-standing structure, covered with plywood and a waterproofing/resistant/wicking/other material, before the brick "walls" were added.

One of the biggest differences between cement and mortar is typically the lack of aggregate (sand) in cement. If your mixture contained sand, you probably used the mortar as intended. The sand exists, essentially, to give the cement something to stick to, just like rocks do for concrete. Without the sand, I suspect that the cement will eventually loosen, crack, and fall away much sooner than mortar; it also will not prevent movement of the bricks in the same way mortar does, because the "connection" that the provides is missing.

If you cannot determine that your brick is solely cosmetic, I would recommend that you remove the cement and replace the bricks using mortar. When in doubt, consult a professional about your specific situation.