"We scored two very good goals and we're delighted about the win. In terms of the character and desire and the will to win we were exceptional," he told Sky Sports News.
"They were throwing everything at us at the end but we stood up and made challenges and Simon Mignolet made an incredible save to touch it on to the bar. The three points was the most important I think.
"We had Luis Suarez here last year and it was a similar kind of game. We showed the capacity to dig deep. Southampton played well give them credit. To get the win was very important."
Sturridge has revealed that he is ready to take on the extra pressure this season following the departure of Luis Suarez.