"Our level has to be between seventh and 10th in the table," Benitez, who side failed to win any of their first 10 league matches this season but have rallied to rise to 12th, said.
"I am the manager until 30 June. We can see the potential. When you see the teams between seventh and 15th, we have to compete with them."
Former Liverpool and Real Madrid boss Benitez is clearly frustrated at the level of investment being made in the playing squad and is likely to want a hefty transfer kitty from owner Mike Ashley over the summer.
Newcastle did break the club's transfer record to sign Paraguayan forward Miguel Almiron in January but were outspent by the majority of top-flight clubs last summer.
Such has been Benitez's impact on Tyneside, he would not be short of job offers should he decide to jump ship.
Asked about the win over Southampton, Benitez said: "Today, we will enjoy it. In an ideal world I want to compete for something. That's the main thing.
"If you analyse the transfer fee and wage bill, it's far away. We'll keep preparing the team and see."
With three games left Newcastle now have a mid-table finish in their sights, something that seemed highly unlikely when they managed three points from their opening 10 games.
Midfielder Matt Ritchie said Benitez had kept the belief in the squad, even when things looked bleak.
"Everyone knows we had a sticky patch at the start of the season but togetherness and desire got us through," he said.
"Of course we want (Benitez) to stay but that's down to him and the board. We can't affect that."
(Reporting by Martyn Herman; editing by Tony Lawrence)
