Because the US has a president who is voted in separately from its legislature, and where the President forms his/her own power centre.

In the UK, Canada, Australia, and other countries, there's no separation between the executive functions of the government and its legislative bodies. The Prime Minister is simply the leader of the party which currently controls Parliament, and his/her ministers are also drawn from parliament. So you have members of Parliament acting as the bosses to a whole bunch of bureaucratic (executive) bodies which take actions on the ground.

In such a system, the minority parties' leadership also assembles a "shadow cabinet" which represents how they would assume power if, ever, they were to to do so. This makes sense because all of the leaders are elected to the legislature anyway, so everyone's already in the government. In some cases, the current government could even fall and be replaced by the shadow government -- something like this could potentially have happened in Canada in 2008.

On the other hand, in presidential governments such as the US, France, and others, the presidency is elected separately from the legislature and represents a separate power bloc. So the president of the US can choose anyone at all for his/her cabinet, not just members of parliament. The losing presidential candidate has no particular role in the government, and so it doesn't make any sense for this person to also create a government.

Hope this makes sense!

(Edit: Removed a reference to a recent election. I left the other one there for clarity because I do not have a handy example of something like this happening outside of 20 years.)

I have a follow up question: Why did America reject the parliamentary system of the British and make up a whole new system?

The closest version to a Shadow Cabinet in the US are leadership roles held by the minority party in the House and Senate. For example, right now Nancy Pelosi and Chuck Schumer are the minority leaders in the House and Senate, respectively. Under them are other minority leadership positions like minority whip and a whole slew of ranking minority members in each congressional committee. Should the minority party win a majority in their chamber in the next election, usually, but not always, the minority leadership shifts over to assume majority leadership positions. So House Minority Leader Pelosi would almost certainly become House Speaker, the minority whip will become majority whip, and usually but not always the ranking minority members become committee chairmen. The comparison doesn't work perfectly because the US doesn't have a parliamentary system so the idea of a shadow cabinet is less important.