City supporter here, quite fond of Everton, posted occasionally for a few years.
Thought you were superb yesterday. Congratulations on the three points. Looked like a proper team to me after some patchy results. Felt like watching Everton again for the first time in quite a while. The boy Davies in midfield is clearly a special talent, but we knew that before yesterday (if only someone would've told our midfield!). That result should prove a pivotal one for Koeman i think. A fair amount of Toffees i know haven't been sure about him, but he's always looked a good fit for the club to me, and with a couple of transfer windows and time to get his ideas across he'll do well. I'd expect you to finish clear in 7th now, but if you can put a run together who knows, neither Manchester club looks uncatchable. More important than exactly where you finish, though, it provides a good chance to really bed these young players in ahead of next season.
As for us, well, we're sadly seeing a few years of off-the-pitch mismanagement catching up with us. The majority of our supporters have quite a simplistic, short-termist view of it, but the reality of it is the current Director of Football (Txiki Begiristain) has a horrendous record for signing players (Fernandinho and De Bruyne his only clear successes), and moreso for selling them (Tevez, Barry, Dzeko, Hart - all players who made the difference when the side wasn't playing particularly well). The upshot of this is Guardiola's walked into a squad with no defensive leaders, over-the-hill full-backs, and a malfunctioning engine room. Not that i don't think the manager's failing to show a lack of smarts, but like Koeman i'd sooner judge him in time and own team. Overall, though, i don't think it's a bad thing for our supporters to temporarily get dragged back down to earth with a bump, sometimes a step back to take two forwards is necessary.
Anyway, good luck for the rest of the season (especially in the away games at the Emirates, White Hart Lane, Anfield and Old Trafford!), and all the best to you all.