The Shulchan Aruch,[1] in discussing the case of a ba’al koreh who missed a pasuk, makes the following distinction: If the omission occurred during a weekday kri’at haTorah, then as long as the minimum number of p’sukim were read, we need not go back to read the omitted pasuk. However, on Shabbat morning, we must go back and read the omitted pasuk together with two adjacent p’sukim.[2] If need be, this is done even after the sefer Torah has been returned to the ark. Most poskim rule that we do the same even if just a single word was omitted.[3] The regular birkot haTorah are recited before and after the three p’sukim.[4] However, if we become aware of the mistake right after the aliya where it occurred, then we do not need a separate aliya, rather, the next aliya starts from the place of the mistake and continues into the reading of the next aliya.[5] If the pasuk in question is within three p’sukim of a break in the Torah text (p’tucha or s’tuma), we start reading from the beginning of that section.[6]
Your case is more complicated in that the Shulchan Aruch’s ruling was not employed immediately. The question is whether Mincha is a suitable time to make up the omission, and, if so, how? There is little discussion of this matter amongst the classical poskim, but the following approach emerges from our analysis.
There is a general machloket between Sephardic and Ashkenazic poskim as to whether a community can read the weekly parasha at Mincha of Shabbat when they were unable to do so at Shacharit. Sephardic poskim do not suggest doing this,[7] whereas Ashkenazic poskim do.[8] Therefore, Rav Yosef[9] says that if a Sephardic congregation missed a pasuk and did not act on it prior to the end of the Shabbat morning services, they should read that pasuk at the beginning of kri’at haTorah on the next Shabbat morning along with three adjacent p’sukim. It follows from that approach that Ashkenazim could do the same at Mincha: read the problematic pasuk and perhaps two others, and then skip to the beginning of the next Shabbat’s parasha during the same aliya. This is preferable to reading three p’sukim with berachot from the morning’s parasha independently of the new kri’at haTorah. Since there was a complete set of seven aliyot,[10] some would say a separate reading with berachot is unnecessary[11] and, therefore, it is better to attach the makeup p’sukim to the reading for Mincha.
The fact that you read straight from the place of the mistake until the beginning of the next parasha was, in some ways, halachically preferable (see the Sha’ar Hatziyun cited in n. 5, which may be applicable here). However, it was apparently unnecessary and is not recommended because of tircha d’tzibbura (public inconvenience). B’di’eved, though, your solution was effective for an Ashkenazic community and was reasonable under the circumstances.