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Answer: The mishna (Mikvaot 10:1) says that if one puts a kli (utensil) into a mikveh upside down, it is an invalid tevilla. This is due to the air pocket that prevents water from coming in fully. While this seems to invalidate your tevilla, a further look shows that matters are not so simple.
The Kiryat Sefer (Mikvaot 3) is unsure whether the above problem is that the water must come over the entire kli, in which case there is a Torah-level problem. The other possibility is that the problem is chatzitza (something that separates between the water and the object that requires tevilla). Regarding chatzitza there are two main parameters: whether it covers most of the object; whether it is makpid (one does not want to leave the chatzitza there indefinitely). When both factors are stringent, there is a Torah-level problem; when one factor is stringent, there is a rabbinic problem (Eruvin 4b). If the problem is that an air pocket is a chatzitza, since water touches the whole outside and some of the inside, the problem is at worst rabbinic and one must assume that it is considered makpid.
First, let us see if it is possible to require that the water touches the whole kli. If so, how could a chatzitza on a minority of the kli be fine from the Torah and permitted if one leaves it there forever? One approach is that in such cases, the chatzitza is batel to (undistinguishable from) the body/object, and it is as if the water touches everything (Sidrei Tahara, Yoreh Deah 198:1). However, the more convincing approach is that the water is required to touch only the majority of the surface, as long as the whole object is submerged and thus enveloped in water, and one has to deal with the issue of chatzitza (Chazon Ish, YD 95:3; see Badei Hashulchan 198:27).
According to the second approach, one could ask if something as "ethereal" as air can be a chatzitza. There seems to be a machloket whether something porous is a chatzitza. On one hand, mishnayot (see Mikvaot, ch. 9) indicate that liquid objects on a surface are not a chatzitza, whereas their dried-up counterparts are. Yet, the mishna (Mikvaot 10:6) says that tevilla on a barrel full of a not water-like liquid is invalid, and thus liquid must be a chatzitza. Tosafot (Zevachim 78b) says that a little liquid (the former cases) is permeable, whereas a barrel full is not (see Biur Halacha to OC 161:1). Others say that thick liquids are not considered permeable, and the reason some liquids are not a problem is that they are not considered makpid (Shach, Yoreh Deah 198:19; see Rama, YD 198:14). If so, an air pocket, which is not permeable when the kli is at certain angles, seems problematic.
At this point, any way we understand the mishna opposing upside-down tovelling should render the tevilla in question invalid. Yet, the Shulchan Aruch (YD 202:6) says that if the kli is somewhat wide, the tevilla is valid because water gets to its bottom. The Bach and Taz (ad loc.) argue that even wide pots can have air pockets, which experimentation and scientific analysis (we did both) corroborate. Perhaps Rav Yosef Karo assumed the following. There is not a need for water on the entire surface, and air does not function like a chatzitza. It is just that a type of tevilla that is not close to getting water throughout is not a proper tevilla. However, with a great width to height ratio, even when the angle is slightly off totally upside-down, water comes in fully, and it is easier for the water to get to any given spot with minimal swiveling. Thus, in those cases, it is considered a reasonable tevilla, and this likely applies to your case.
Since the simple reading of the sources indicates the tevilla was invalid, we suggest you to do tevilla again, but without a beracha. If it is difficult, there is some room for leniency (including for reasons beyond our present scope).
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