Or we just don't have the same international brand?
For most of the adults who are making decent incomes atm, Inter wasn't a big club, not when compared to Milan in the 90s and early 00s. Our one major crowning moment in the international stage in recent memory was extremely poorly exploited by Moratti - to the point where our commercial revenues the season after were the same as the one before!
For all the major years of mass globalisation, we were only really a decent club of note post Italian scandal which also coincides with, for example, significantly reduced presence of Italian football on UK TV.
Our brand value is just way lower than Milan. I know we don't want to believe it, but it's the truth
That's not the reason though.
Milan is more popular because they won 5 European Cups and appeared in a few more in the span of 20 years.
Juventus is also more popular because they also were CL finalists in the 90s and early 2000s.
Inter played mostly in the Uefa Cup and didn't have CL success, had top players like Matthaus, Ronaldo, Adriano etc that everyone considered top 5 at any moment and there was exposure, but results didn't invite any appreciation. The reason is mainly media.
It's not easy to measure the amount of [international] fans that genuinely watch games and follow the club. These modern metrics of social media aren't really a good giveaway as they create some bubble and you think that it represents something. Like Lebron James for example appears to be the most popular NBA player of all time now but if I pick 1,000 random people from 150 countries, I bet you that the recognition level would be under 10%. Do that 25 years ago with Michael Jordan and the recognition numbers would be more like 70%.
Same way, we have less social media following but the reason is mass media is pretty much instructing that at some level. Mass media decides which CL game a person will have available. And mass media or culture would decide which games would be broadcast at public spaces in CL nights. And let's be honest, even during the height of the popularity of Serie A, most people followed it via local media the next day rather than watch games.
And at least on Europe, where the majority of football fans caring about European football were, having a foreign team was secondary, unlike the modern trend. Domestic football had all the interest unless it was European nights. Now the media still tries to keep it that way but the kids don't follow that much.
There was interest in Argentina but not as high as now, limited in Brazil, and almost non existent in most of Asia which started to rise in the 90s. There was significant amount of followers but nothing like now. Australia and the USA, at least in regards to Serie A, were only linked via expats or immigrants (whatever generation).
And this is the generation you're referring to. Casual viewers, video game players (early FIFA games, ISS and PES, Championship Manager and early 2000s more came out) who picked teams they claimed to support based on limited exposure. I even know people who picked teams based on followingn them on the freaking Teletext! Others pick them because of players, or the jerseys colors etc. Others later due to betting.
But this sort aggressive attraction internationally is something novel. And that's why we're missing out in the younger generation as well, since we were irrelevant in their formative years.
And we didn't gain a lot of fans in 2010 imo because of the Mourinho factor. Already a love or hate character, at a club that by the time had top players but was considered underperforming, shortly after the Calciopoli (whereas Milan won CL the following year and paraded that as a success despite getting penalized for corruption!) so everyone assumed winning in Italy was easy, even if 2/4 were won on the final day. So there was no ground for momentum.
Even now, we reached CL semis but as you claim we had an "easy path". That is nonsense. We didn't have an easy path. We had a less commercial path.
If we reach CL final now and beat Atletico, Cit and Real to do it, even if we lose the final, it'll give us a greater platform. Not because we're better or because Zhang/Antonello do a better job than Moratti and his directors. But because there would be more witnesses.
Even if we had beaten City it wouldn't do much last season in terms of popularity. We need to do this over a decade with at least 4 CL trophies if we want to reach the heights we think we deserve and I'm not even kidding. This is how modern football is shaped, you need to be always relevant and at the top. The competition at the very top is thin, and as long as you're part of it, you're in commercially. At the moment we're not in.
And if we want Serie A as a whole to get some coin, then Milan has to be in as well, Juventus has to be in, Roma/Napoli/Lazio at least someone else needs to be in. Italian teams need to dominate the two "minor" cups as well. That's how you bring popularity up.
It's not a nice business and not really a self sufficient one. And money doesn't rain because a director did a better dance than his predecessor.