The win sends Inter seven points clear at the top of the Serie A table.
Argentina striker Milito said: "I scored a very important goal, we are happy because we have three points that would stretch the gap from our direct competitors in the standings. We had some difficulties in the first-half, also because Livorno were good at putting us in difficulty, but in the second half we knew how to manage the game well.
"Now we look to the decisive match with Dynamo Kiev in the Champions League. We are aware that it will be an important game."