England, who face North Macedonia in Skopje on Monday, are all but assured of being among the top seeds in next month's draw for the finals in Germany.
But they were disappointing in Friday's 2-0 victory against Malta at Wembley and will be keen to improve against lowly North Macedonia, whom they hammered 7-0 at Old Trafford in June.
"Qualification's done," the England boss told British media ahead of the Group C finale.
"With the games at the weekend, we might be ranked third in the world at the minute (England are fourth in the latest published FIFA rankings), but we're two places off where we need to be so we can't waste games.
"Some of the players have got three games to get into a squad, some have got maybe three to get into a team."
Southgate said the level of performance had to be "spot on every time".
World Cup winners Argentina are top of the rankings, with France in second place and Brazil third. England have been in the top five for five straight years.
Asked if being number one drives him on, Southgate said: "Yeah, because ultimately you achieve that through consistency and you've got to play well in the tournaments as well because the ranking points are higher in the tournaments.
"Also, it sets behaviours every day on the training pitch, off the training pitch.
"If you are going to be the top-ranked team, there's no room for sloppiness or casualness. That's got to be our drive."
England's final camp of the year has been disrupted by absentees.
Five players withdrew from the original squad through injury and two more departed the squad before they flew to the Balkans.
The Football Association announced Kieran Trippier had gone home due to a personal issue, while injury meant Jarrod Bowen left the camp on Sunday.
