Adam Lallana's second-half strike proved the difference in what was for the most part a dull and frustrating encounter at St Mary's.
Downing confirmed Mel - who has yet to meet the players and watched from the stands - did not give any pre-match instructions.
"I saw Pepe yesterday which was nice," Downing said.
"It was a good conversation, he is a warm man and wants to put some good ideas across, so I look forward to working with him next week."
Asked what he would have made of the match, Downing added: "I think he would have seen us an organised side.
"Without the ball we restricted Southampton to not many opportunities, not clear-cut opportunities anyway.
"We are all disappointed about what we did with the ball. We were frustrated and credit to the opposition, they don't give you time and quickly press you as soon as they lose it.
"When the goal went in we changed shape and threw a little more caution to the wind and it opened up and we got more into the game as it progressed.
"I think he will work on us in terms of possession and creativity but I thought there was commitment in terms of the team defensively."
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- Adam Lallana