Sky have only ever shown themselves adept at one tactic: the simple bludgeoning tactic of getting on the front and riding too fast for anybody else to attack. This worked in the sprint when Cavendish was at the team for the same reason it did at HTC - they kept the break on a tight leash until it was time to lead the sprint out, then rode so hard nobody could get away. This works in the mountains doubly so because they set a pace so high that they burn everybody else off the back. And then, they have the strongest climber at the back of that train, so once he feels the time is right he's in the perfect position to launch his attack.
In the Classics, however, that's much harder to do. In a stage race, the break often consists of GC no-hopers and break specialists in small groups; once the péloton is happy with the composition of the break, they just let them go, then start reeling them back, and leave them out there until close to the end; while there's a break up front that they've missed, most riders will sit back in the bunch feeling that their stage win chances are gone for the day and they'll preserve energy to try and get into the break the following day. In the Classics, much more dangerous riders will want to get into the attack groups, and you will regularly find that because it's imperative to be near the front at narrow or steep sections, a lot more jostling to be at the front and a lot less willingness to allow one team to dictate the pace. This means that it is unlikely that a team will be able to mass rank at the front, and then as soon as there are punctures, accidents, the wind blows and the riders form echelons, or simply a couple of riders who can't hack the pace but due to the narrow road are holding a lot of people back from staying with the pace of the leaders, you get the situation where the race fragments, and because few teams are able to gather all their forces together in one place, riders have to do a lot more work alone or in small groups than they ever would in stage races unless they were in the break of the day group.
Sky's one successful tactic works very well, as long as they have either 1) a numerical advantage; 2) the strongest rider for the style of finish. In the Classics they do not have anybody who classes as #2, so they need to fashion #1. And they to date have not shown the capability of providing such a situation, with very few exceptions. A notable exception would be Paris-Roubaix 2012, where a number of Sky domestiques failed to catch Tom Boonen riding solo. A lot of the reason for this was that of the 3-4 Sky riders in the bunch, Ian Stannard was the most tired, having done a lot more work on the front earlier in the race than the others; as he was likely to be the first to drop, the team put him on the front and then toasted him; he couldn't keep up with Boonen because he was shattered, so the gap got bigger, and the other Sky engines were left with too much to do when Stannard's tank finally hit 'empty' (and you will know it takes a lot of effort for Ian Stannard's tank to hit 'empty').
Sky have plenty of riders who would be capable of winning in the Classics. However, unlike in the stage races, they do not have any who can win by being the strongest unless there are some very crash-decimated fields, so they have to rely on winning by being the smartest; thus far, I'm afraid for Sky fans, they have not shown that this is in their repertoire.