From a sports perspective, it is important. I'm a Juventus fan, we recently won 9 straight Serie A titles, 4 straight League Cups, but something is missing, the UCL, we lost it twice, against two better teams, but teams that we were able to beat in other occasions, that streak is tainted in the eyes of the fans because we couldn't win the UCL, considering, also, that we basically had no competition at home. The same goes for the Juventus of the 90s, losing two finals, against two weaker teams, has tainted the memories fans have of that team. It's always "Yes, we won, but the UCL..." or "Yes, what a great team we had, but we lost two finals...".
It's also a matter of country, football media is very local, so for example in Italy they did report City winning, they did report that it was almost an unstoppable machine, but that's pretty much it, the same for any other non Italian team.
I am not from the UK, I have no explanation why the British press is not giving City the same kind of attention they gave to United, could it be that, if I'm not mistaken, Manchester United was the first English club winning the UCL and the first club to win the former European Cup since the 80s ban?