It's not exactly as straight forward as that, tactically speaking. United played with a high defensive line and also pushed high up the pitch. If LFC opted to push out fully like theyhadto in the 2nd half, the game would have been very stretched, end to end, and I'd suspect play into Uniteds favour even more so, given Sturridge wasn't on the pitch yet.
There were instances where that was the case in the first half, because when challenged, Carrick & Cleverly & Kagawa were excellent in retaining and building possession. United looked like scoring either way, you can just say Rogers perhaps bottled it with his starting selection, rather than how the team played in the first half.
Also, the subs definitely went in favour of LFC. Surprisingly Valencia is having a poor season and continued to this game, often giving away possession. Similarly, with Jones swapped in for Kagawa, with his role some what 'Follow Suarez', the midfield battle after an hour of play had gone in favour of LFC. United had to take a much deeper defensive line and it was all to do with parking the bus to keep it at 2-1, not aiding in any way whatsoever for calming nerves around OT. Commentators would have suggested that it would have been wiser for likes of Scholes instead of Jones (if he made the bench wtf..), or Giggs for Young with Welbeck dropping right, etc. But either way, it worked out, 2-1 was the final score, so I guess I can't complain.