Playing a more 'English' style can cause problems
It's a cliche to suggest continental sides struggle against physical or direct football, but against highly technical sides such as Bayern Munich and Barcelona, this is where English clubs' comparative advantage lies.
Bayern are a more powerful side than Barcelona, but they had no answer to Arsenal's extremely forceful start at the Emirates, seemingly unable to deal with the tempo. Only Mesut Özil's penalty failure prevented Arsenal from leading.
Barcelona, meanwhile, still struggle aerially. They were comfortable defending against a half-fit Sergio Agüero running in behind, but encountered more problems when facing the taller Edin Dzeko, who allowed City to cross the ball dangerously, and forced Víctor Valdés into a great save with a header.
It isn't in Arsène Wenger or Manuel Pellegrini's mindset to play route one football, but a direct approach makes sense against this opposition.
Individual mistakes are costly when dealing with through-balls
Bayern Munich and Barcelona are the finest examples of teams successfully using an aggressive defensive line. They concede space in behind, but when forced to turn and chase opposition strikers, their challenges are usually controlled.
In stark contrast, the English clubs committed first-leg fouls which denied a clear goalscoring opportunity: resulting in a penalty, a red card and a suspension. Martín Demichelis brought down Lionel Messi, Wojciech Szczesny did the same to Arjen Robben a day later.
It comes down to decision-making, and while it's easy to claim in hindsight, Demichelis and Szczesny might have been better off pulling out of the challenges, rather than handicapping their side for the remainder of the tie.
You must strike when on top
Both Bayern Munich and Barcelona enjoy a staggering level of control at one point in any game – but there's also a spell when the opposition had chances, too.
For Arsenal, this was at the start of the first leg and the end of the second leg, supporting the idea that Pep Guardiola's sides take a while to get started, and can become complacent. City, meanwhile, had some decent opportunities midway through the second leg at a nervous Camp Nou.
The key, of course, is scoring during these periods – and when the pressure is on. Arsenal only struck once Bayern had gone 3-0 up on aggregate, an outcome replicated by City. Had they taken earlier chances, these ties would have been closer.
You need 100% fit players to press
It was understandable that Wenger and Pellegrini wanted Özil and Agüero to feature in the away legs, but neither looked fully fit – and fresh, energetic players are vital against Bayern and Barcelona.
Both sides are excellent at holding on to the ball, particularly in deep positions, and the fact they were happy to cool the tempo of the second legs, preserving their advantage in the tie, meant the English sides had to press high up the pitch to force the issue, and open up the game.
This was difficult carrying a half-fit player, and both managers were forced to waste a substitution at half-time, giving them less opportunity to inject energy in the second period.
Weaknesses in squad are exposed at this level
The glaring holes in Manchester City and Arsenal's squads haven't been a significant issue in the Premier League, but they were unable to disguise their weaknesses against Europe's best.
City's lack of a commanding centre-back to play alongside Vincent Kompany proved decisive in both legs, while Arsenal's absence of a trusted alternative to Olivier Giroud meant the extremely raw Yaya Sanogo started the first game. Two goals City conceded were directly because of centre-back errors, while Arsenal gave themselves an extremely tough task in Munich, having failed to take full advantage of their early dominance at the Emirates.
City's problem in defence has been clear for months, while Wenger was keen to sign another striker last summer. These problems must be addressed.