The Dutchman thinks his side can continue their push for Champions League qualification.
The Saints saw off Newcastle on Saturday evening thanks to two goals from loan-signing Eljero Elia, extending their unbeaten run to eight matches in all competitions.
The result also saw them move back into third in the Premier League table - and Koeman believes his side can prove the doubters wrong and qualify for the Champions League.
"I think we can keep this position," Koeman told Sky’s Saturday Night Football.
“We have a lot of confidence - that’s the key for the results in the last few weeks.”
The Dutchman was full of praise for his side as they had to defend against heavy Newcastle pressure in the closing stages to secure victory.
"It was a great performance from the defence to win again," Koeman added.
"They [Newcastle] didn’t create a lot until maybe the last 10 or 15 minutes. I think we deserved the win because in my opinion the better team won today."
The win at St James' Park was the Saints’ third on the bounce during a run which has seen them beat both Manchester United and Arsenal, while they drew with Chelsea before their defeat of the Gunners.
That run, against their Champions League rivals, has been all the more impressive considering they are without regulars Morgan Schniederlin, Victor Wanyama and Jay Rodriguez.