You won't be able to get it stamped. However, the lack of a stamp only results in a presumption that you have overstayed, a presumption that may be rebutted with other evidence. The chance of this actually causing a problem is quite small, but you could reduce it further by keeping with your passport any evidence you have of your departure from the Schengen area or your entry into the UK (or wherever else you might have flown to on October 16th). If you want to be really well organised about it, you can type up a brief account of your experience with the e-gates and keep that together with your evidence.

You won't be able to get it stamped. However, the lack of a stamp only results in a presumption that you have overstayed, a presumption that may be rebutted with other evidence. The chance of this actually causing a problem is quite small, but you could reduce it further by keeping with your passport any evidence you have of your departure from the Schengen area or your entry into the UK (or wherever else you might have flown to on October 16th). If you want to be really well organised about it, you can type up a brief account of your experience with the e-gates and keep that together with your evidence.

Here's the relevant article of the Schengen Borders Code as it currently stands on October 21, 2024:

Article 12

Presumption as regards fulfilment of conditions of duration of short stay

1. Without prejudice to Article 12a, if no individual file has been created in the EES for a third-country national present on the territory of a Member State or the entry/exit record of that third-country national does not contain an exit date following the date of expiry of the authorised length of stay, the competent authorities may presume that third-country national does not fulfil, or no longer fulfils, the conditions of duration of authorised stay within the territory of the Member States.

2. The presumption referred to in paragraph 1 of this Article shall not apply to a third-country national who can provide, by any means, credible evidence that he or she enjoys the right of free movement under Union law or that he or she holds a residence permit or a long-stay visa. Where relevant, Article 35 of Regulation (EU) 2017/2226 shall apply.

3. The presumption referred to in paragraph 1 may be rebutted where the third-country national provides, by any means, credible evidence, such as transport tickets or proof of presence outside the territory of the Member States or of the date of expiry of a previous residence permit or long-stay visa, that he or she has respected the conditions relating to the duration of a short stay. In the case of a rebuttal, the competent authorities shall create an individual file in the EES if necessary or indicate in the EES the date on which, and the place where, the third-country national crossed the external border of one of the Member States or the internal border of a Member State not yet fully applying the Schengen acquis but operating the EES in accordance with Article 20 of Regulation (EU) 2017/2226.

4. Where the presumption referred to in paragraph 1 is not rebutted, a third-country national present on the territory of the Member States may be returned in accordance with Directive 2008/115/EC of the European Parliament and of the Council ( *5 ). A third-country national enjoying the right of free movement under Union law may only be returned in accordance with Directive 2004/38/EC.

Article 12a concerns the transitional details for the impending implementation of the electronic entry-exit system, EES.

As noted in the comments, this doesn't apply to Ireland, which has opted out of the Schengen area and related provisions (by contrast, a number of provisions of the Schengen Borders Code and Schengen Visa Code do apply to other non-Schengen EU states, for example the list of visa-exempt nationalities).