Mignolet and co will not have to wait long for an opportunity to taste victory once more, though, with a tantalising Capital One Cup clash against rivals Manchester United on the schedule for Wednesday.
"We wanted to win the game, especially when you play at home at Anfield against Southampton you want to get three points," the Belgian told Liverpoolfc.com.
"They came here, blocked us off and were really organised - which made it difficult for us to play and create chances. If you then concede in the second half, it's a disappointment.
"We've got another game on Wednesday, when we can put things right straight away; I think it's a perfect scenario to get back to it. We have a decent game to look forward to and everybody can put things right.
"Sometimes you have a disappointing result, but then you have to make sure the result and performance afterwards is back on top."