A superb strike by substitute Matej Vydra clinched a 2-1 success on the south coast on Saturday to make it three victories from four Premier League games for the Clarets.
It secured back-to-back away wins for Burnley after their shock triumph at Manchester United last month and took them further away from the relegation zone.
At the beginning of January, Burnley were on a poor run of form but have turned things around and silenced the doubters, plus those who have labelled them a "long-ball side" or a team who play "anti-football" as now-Arsenal defender David Luiz insisted last season.
Dyche, when discussing the win, pointed out: "Ironically the (Southampton) programme said Sheffield United have played more long balls than us and yet they are definitely not long balls, but I am not really worried about it and I know Chris (Wilder) is not.
"He will not mind me mentioning that because he is a fantastic fella and look at the job he is doing so he won't mind me saying that and it was in the programme.
"A good technical analysis in their programme, I quite enjoyed that. I told the lads and said, 'there you go, that is what they think of you' and it is always lovely when they give you that little edge to work on. I love that."
The three points for the Clarets on Saturday has lifted the Lancashire outfit up to 11th place in the table and level on points with Arsenal after 26 games of the Premier League campaign.
With five points between themselves and the top six, Burnley will look to narrow the gap on Saturday when they play hosts to strugglers Bournemouth at Turf Moor.