It's interesting to look back. On purely achievements you can't really class him as a failure - 6 years, 1 champions league win and an FA cup win is more than they'd done in the 6 years before (Champions League > League Cup and UEFA Cup for my money).
His transfer dealings and man management were poor, that goes without saying. He really lost the plot towards the end (really trying to flog Alonso for Gareth fecking Barry was the start).
His best achievement would really be that 08/09 team. If he (and his team) didn't bottle it post fahcts gate, or if they'd been up against a team that wasn't one of the best teams we've ever had, they would probably have won it. So yeah
Torres
Riera Gerrard Benayoun
Mascherano Alonso
Aurelio Carragher Hyypia/Skrtel Arbeloa
Reina
is probably his best achievement. Unfortunately selling Alonso ripped the heart out of that team, not just playing wise but leadership wise aswell (go back to Marsh 2008 when Mascherano got sent off at OT, it was Alonso trying to tell him to calm down and hold him back, while Steven Gerrard stood off to the side a bit).