This is an age old question. The verse you ask about is Numbers 10:10:
וּבְיוֹם שִׂמְחַתְכֶם וּבְמוֹעֲדֵיכֶם, וּבְרָאשֵׁי חָדְשֵׁיכֶם וּתְקַעְתֶּם בַּחֲצֹצְרֹת עַל עֹלֹתֵיכֶם וְעַל זִבְחֵי שַׁלְמֵיכֶם; וְהָיוּ לָכֶם לְזִכָּרוֹן לִפְנֵי אֱלֹהֵיכֶם אֲנִי יְהוָה אֱלֹהֵיכֶם.
Also in the day of your gladness, and in your appointed seasons, and in your new moons, ye shall blow with the trumpets over your burnt-offerings, and over the sacrifices of your peace-offerings; and they shall be to you for a memorial before your God: I am the LORD your God.
This verse not only doesn't mention the Shofar or Teruah, its verb of Tekia is specifically about a trumpet.
Let's review some rules about the verses to use:
- The minimum is 3 verses each of Torah, Tehillim and Neviim but one can add more.
- Ideally we should finish with a Torah verse, but if we didn't we still fulfill our obligation.
- A verse that uses the verb פקד as a Remembrance counts for that section.
- A verse that mentions just Teruah ("תרועה שאין עמה לא כלום") such as Num 29:1 counts as a Shofar-verse without the word "Shofar".
- A verse that mentions a Shofar theme and a Kingship theme can be used twice.
The last three are the positions of R' Yose, though R' Yehuda disagrees. The law follows R' Yose, though at least in the first case the longstanding custom is to be strict to accommodate R' Yehuda's position.
For your verse to count as the final Torah verse, we have to assume that 1) it's permissible to interrupt before the final verse with prayer sequences, 2) against R' Yehuda that a verse with no mention of Shofar counts, 3) a Tekia verb is as valid as a Teruah verb, and 4) a verse that explicitly is about trumpets counts as "just Teruah".
Raavyah (536) quotes some who reject 1, but he defends 1 and rejects 4. He explains that there is indeed no need to finish with a Torah verse if you already have at least 10 verses because you added to the others as "we" do. He writes this Torah verse was put at the end of the blessing because it fits with the content generally (like many, many other blessings which include content appropriate verses; a common example is the second blessing after bread). This seems to also be the position of the Sefer HaIttur.
Some Rishonim felt you should indeed ideally add a Torah verse right at the end of the main verse section. Rabbenu Yonah and Ritz Giyat added Num 29:1 even though it doesn't have the word "Shofar" relying on the position of R' Yose against R' Yehuda. Ramban added Num 23:21 which also doesn't have the word "Shofar" even though this was already used as a Kingship verse, relying on the position of R' Yose against R' Yehuda on two counts. Rashba (1:481) quotes both these options.
If we didn't want to rely on R' Yehuda, there are exactly four verses in the Torah that actually use the word "Shofar", three of which have already been used. Accordingly, we could use Lev 25:9. Seemingly, this solution wasn't chosen because it feels odd to say on Rosh Hashana, though technically it should work and it indeed must have been used according to R' Yehuda. (Shibbolei Haleket (290) and Maaseh HaGeonim (RH 3) write that since there was no other Torah verse available, we are forced to use a non-Shofar verse in order to finish the Shofarot section with some Torah verse; however, this contradicts an explicit Gemara (RH 32b) that there are sufficient Remembrance and Shofar verses in the Torah.)
Rosh (RH 4:3) accepted all 4 assumptions and defended counting Num 10:10 even after an interruption. He cites a Yerushalmi (that we don't seem to have) that explicitly mentions using this verse at the end of the Shofarot section as a way to mention Rosh Chodesh on Rosh Hashana, but the proof isn't ironclad because the verse, while clearly an old part of the blessing, could be there as Raavyah explained simply as appropriate content. Rambam and many others, by not including any other verse there in their Siddur, appear to have agreed to count the verse. Ritva (RH 32b) too defends counting the verse, noting that one opinion in the Sifrei actually derives the obligation of the Shofarot section from that verse, though he writes it is better to follow his teachers Ramban and Rashba to include Num 29:1 as well.
As mentioned if you don't include a final Torah verse you still fulfill your obligation, so this is a "low risk" sort of problem. On the other hand, if you add an extra verse you still fulfill your obligation, so this is also a "low risk" sort of solution. Ask your rabbi what you should do.