Are you sure? Most would plame the Penitus Oculatus, not Tullius.
The emperor double was killed in Castle Dour...Tullius' castle. His own stronghold was infiltrated by the Dark Brotherhood! Then the real emperor was killed off the northern coast in Haafingar; Tullius' immediate area of responsibility. While the Penitus Oculatus is directly responsible for the emperor's immediate safety, Tullius is responsible for maintaining stability and security in the region. External and internal security--you don't think the two work hand in hand? If a general doesn't have his soldiers guard a perimeter and a horde of assailants overwhelm the head of state and his bodyguards, do you think the general will take the blame? At the very least, Tullius is just as culpable as the inept Penitus Oculatus.
The dude that ordered his assassination was an Elder Council member, and claims that others were of the same mindset. And the politics in Cyrod would suggest that Mede's death would be welcomed.
That is certainly up for debate. Very interesting developments but in all likelihood the Elder Council, whatever their intentions, would have little use for a failed general, commissioned by Emperor Mede II. In fact, if it were true that the Elder Council were anti-Mede, they would likely seek the death of Tullius.
Hadvar also implies that Tullius had only arriveed in Skyrim fairly recently, so I'd give Tullius a bit more credit considering what he has accomplished.
You and I might give him credit but do you think the politicians, fickle and reactionary as they invariably are, that sit on the council will care about that. Its like a president that is elected to office and inherits the problems of the nations, he/she is now responsible for them.
And aren't you forgetting who else was a very competent general?
In the Imperial army? I can't think of any right now.