If one omitted אלקי נצור in Shemoneh Esrei does he have to repeat Shemoneh Esrei?
Even though there is special significance to the single line "yih'yu l'ratzon...", which is meant to be appended immediately after the end of sh'mone esre (Shulchan Aruch Orach Chayim 122:1), there is no requirement to say the other short prayers that often come after it. For an incidental proof of this, see the words of the Shulchan Aruch in Orach Chayim 122:2 -
וּמִיהוּ הָרָגִיל לוֹמַר תַּחֲנוּנִים אַחַר תְּפִלָּתוֹ, אִם הִתְחִיל שְׁלִיחַ צִבּוּר לְסַדֵּר תְּפִלָּתוֹ וְהִגִּיעַ לְקַדִּישׁ אוֹ לִקְדֻשָּׁה, מְקַצֵּר וְעוֹלֶה, וְאִם לֹא קִצֵּר יָכוֹל לְהַפְסִיק
...however, one who is used to saying supplications after his prayer, if the sh'li'ach tzibur started his [public] prayer and reached kadish or k'dusha, [the individual may] abbreviate and finish, and if he hadn't abbreviated he may interrupt... (emphasis mine)
First, notice that it refers to the supplications that are the topic of this question as coming "after" the t'fila, which is a clue that they are not part of it and therefore would not be subject to the rules of compensatory prayers. But mainly, it is clear from this that one need not say them all (at least not every time, according to the Mishna B'rura below) even if it is generally his custom to do so.
מקצר ועולה - דהיינו שמפסיק באמצע התחנונים ופוסע לאחריו דאין חובה לומר תחנונים בכל פעם ואם אין לו שהות לפסוע ולא אמר יהיו לרצון קודם אלהי נצור טוב שיאמר עתה יה"ל קודם שיענה עמהם