The Northern Ireland captain scored the second goal of the game as Saints recorded their first victory under new manager Mauricio Pochettino.
And, while Davis was understandably delighted with the result, he was keen to warn against losing sight of the task in hand.
"It is a massive three points for us – especially against Man City – so we can take a lot of positives from that," he told Saints Player
after the game.
"But it’s important we don’t lose sight of what our aim is – and that is to stay up first and foremost, and then we'll see where we can go from there.
"We know what we have to do. We have shown that we can get a level of consistency in our performances over the past few weeks so now we have to see that through.
"We won't get carried away because we are all aware of the effort and level of performance that is required between now and the end of the season."
Today's goal was Davis's second of the season – ironically, his other came against City on the opening day of the season.
And he credits a change of playing style under Pochettino for how today's strikes came about.
"I think since the new manager has come in he has stressed that he wants us to play a high tempo game," he said.
"We press high up the pitch and I think we got a lot of joy from that today – that is what happened with the first goal when Punch (Jason Puncheon) has nicked it and we went on from there.
"It is hard work playing like that but it is nice to get the rewards from it with three points.
"I was delighted obviously," Davis said of his goal. "I think you have to get into the right positions and hope one falls for you, so I’m pleased to have reacted first and got our second goal."