"I'm not a manager that I'm in a panic because we have now the 12th position in the table," Koeman, whose side beat leaders Arsenal 4-0 last Saturday and then lost 2-1 at West Ham United on Monday, said ahead of Saturday's trip to Norwich City.
"We know our players, we know our qualities and if there is something to do in business it's about how recovered (Graziano) Pelle is in the next couple of weeks and how Jay Rodriguez will come back," he told a news conference.
"These are two strikers, two good players and of course if we don't have them back maybe that's a question to sign a new striker. But not other positions in the team," added the Dutchman.
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"We have enough competition and I am pleased with the rest of the squad."
Pelle, the club's leading scorer this season, will miss the Norwich trip with the Italian striker still sidelined by a knee injury that has forced him to miss the last two matches.
Rodriguez, who was due back in January, has not played for two months due to a foot injury.
"He will come back but maybe it takes two or three weeks more," said Koeman. "I think it will be the end of January or early February when he is available to play.
Asked about media reports that on-loan defender Steven Caulker could return to Championship side Queens Park Rangers after making just one league start for Southampton, Koeman denied that was the case.
"My plans for Steven are that he stays until the end of the season and then we need to make a decision because he is on loan for one season," he said.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
