It took just four minutes for the south coast side to take the lead, as Shane Long took advantage of some poor Newcastle defending.
Graziano Pelle and Victor Wanyama then notched the other two goals for the reds before Andros Townsend pulled one back for the away side.
The victory very much keeps Southampton well in the hunt for European football next season and Koeman spoke to the press following the match.
The Dutchman said: “I’m very satisfied with the first half because we started well with a high tempo.”
The Saints boss felt that the early goal helped his side and made it difficult for Newcastle but added that he felt the Saints should have scored more goals in the second half.
He then added: “It was important to win the game today because it gives you the confidence you need to fight for our ambitions.”
Saints keep up European chase
Koeman is keeping calm about finishing ahead of European rivals Manchester United and West Ham, he said: “We know it’s difficult because a lot of teams are fighting for the same.” The Dutchman was quick to add that though it will be difficult for the Saints, it will also be difficult for the other teams.
Another plus for the reds was the return of Jay Rodriguez, who made a substitute appearance, after being out of action since October, and Koeman was delighted for the striker on his return to action.
He continued: “It is fantastic. He worked very hard to come back.” With Rodriguez now an extra option upfront for Southampton Koeman feels he will help the club a great deal in the future.
He added on the striker: “It’s important for Jay to get that game-time to improve all aspects of football.”
The Saints next match is a tough trip to Goodison Park to face Everton as the race for European football continues to unfold.