Missing Daniel Sturridge no doubt changed Brendan Rodgers' approach against Aston Villa, but there's no telling whether or not it would have had a decisive impact. We can guess that Liverpool probably would have been better and more cohesive in attack, mostly because good players tend to make things better, and that Mario Balotelli likely would have been more involved as part of a forward line that would have at least had one match of experience together rather than zero.
But the guessing's not going to give Liverpool any points, and it's not going to bring Sturridge back from his thigh strain any earlier. Neither is the £200k that the English FA are reportedly providing Liverpool in compensation; awfully nice gesture and pleasant that there wasn't any sort of disagreement and all that, but there really wasn't any other outcome that seemed likely given that the player was essentially forced into training despite voicing concerns that he would need additional recovery time to avoid this exact situation.
What's most concerning in the report from the Mirror is that Roy Hodgson doesn't have any plans to change his methods--which have translated from Malmo to Inter to multiple stays in the relegation zone in the Premier League--to better account for the fitness of Sturridge and others. Casting this as merely "skipping" training sessions discounts the very real reasoning behind it, which would have very likely accounted for Sturridge's fitness in a more responsible and, ideally, more effective manner. Instead Liverpool are without their best striker for at least two and a half more weeks.
His return to fitness comes just in time for the next international break, meaning he'll likely be included in the squad to face San Marino and Estonia. Fun.