The 22-year-old scored the Seagulls' second goal as they beat the European champions 3-1 at the AMEX Stadium earlier today.
Poyet said: "Ashley Barnes was a little bit above everyone today in terms of what we try to do as a team and what we want our players to do on the pitch.
"For the second goal he was the one who cleared the ball from our box with a header from a corner and somehow he got in the box at the other end to score the rebound.
"That is the sort of willingness we want from players. If he keeps doing that, it will be difficult for others to get in the team ahead of him."
Barnes scored 14 goals in 48 appearances last season.