Signing better players won`t be as easy as you seem to think, better players usually are not available without paying over the odds and paying considerably higher wages. All the real top players are already at CL clubs and will not be for sale unless you pay silly money (Ozil), and wages.
Liverpool have been actively trying to reduce their wage bill and the £30m or so CL revenue will not make much of a hole in last years £50m losses (£91m over 2 years). Even with CL, players will always choose to go to United, Chelsea, City or Arsenal over Liverpool (and Spurs), simply because they pay higher salaries.
Only the very biggest clubs and those with sugar daddy owners shop at Harrods, Liverpool will still be shopping in the same shop as Spurs, which is a level below the highest spenders, looking for value and potential.
Roy Rodgers has a poor strike rate on transfers, he has spent £60m NET and wasted most of it.