The 4-0 victory over Newcastle - their 13th of the season - lifted them above their opponents into eighth place in the Premier League and Shaw is adamant there is more to come from the St Mary's tyros.
Seven English players started for Mauricio Pochettino's side, for whom Jay Rodriguez netted either side of efforts from Rickie Lambert and Adam Lallana.
"They are superb every week," Shaw said. "To have all four of the goals to be from Englishmen is superb. It is great to play for a team like this and especially with the way the gaffer likes his full-backs to play high and wide.
"I think that is one of my qualities as an attacking full-back and I think Calum Chambers today was superb. He said to keep playing how we've been playing. We're only going to get better.
"We've got a lot of young players in the team that will get older, get more experienced and improve as players.
"We want to keep on playing how we're playing and finish as high as possible. By winning games like this, which was a big game for us and the fans watching, is a massive boost.
"I wouldn't say they were poor, but I think we had a game plan. We knew how Newcastle played. They like to be physical and get the ball in the air, but I think our two centre-backs they played well today and they kept Papiss Cisse quiet.
"It is great for me and the other three at the back to get a clean sheet. We spoke before the game about getting a clean sheet because we've leaked a few goals recently. To get a clean sheet at home as well was very good for us."