Saints arrived at Portman Road riding the crest of a wave following Sunday's impressive victory at Manchester United.
That win came at a cost, though, with influential centre-back Toby Alderweireld sustaining a hamstring strain which will see him miss up to four weeks.
It means Saints now have just two centre-backs available, while their defensive midfield options have been depleted by injuries to Morgan Schneiderlin and Wanyama.
An adductor strain saw France midfielder Schneiderlin miss the 1-0 win at Ipswich on Wednesday - a match which saw Wanyama pull up with a hamstring injury just before half-time.
"It is really negative because already we have some other injuries," Koeman said.
"I already spoke before the game with Victor and Steven Davis as I had made the decision to give both players 45 minutes.
"Then 12 seconds before half-time, he got his hamstring injury and, okay, you know if it is really a hamstring injury then he will be out for four or five weeks.
"I don't regret playing him
He had some calf problems out of the game against Man United, but he trained yesterday.
"But, okay, we know we have a tough programme and we don't have a big squad to resolve that kind of problem with injuries.
"Schneiderlin has a little bit the same as he had when he came back from the French national team.
"It is an adductor problem in his right leg and he will be out for three or four weeks, like Toby Alderweireld, but, okay, we have a lot of young players."
Those three injuries will seriously test Saints in the coming weeks, starting at Newcastle on Saturday - a Premier League match followed swiftly by the FA Cup clash with Crystal Palace.
Shane Long's first half goal secured their place in the fourth round, with Koeman satisfied by his side's display against Championship promotion chasers Ipswich.
"I think it was a very serious performance tonight," the Dutchman said
"It was lucky we scored out of the first chance we got in the game.
"After that, we defended well, had good organisation in the team.
"I think we had some good opportunities in the second half in the first 10 or 15 minutes to create something out of that counter-attacking.
"But I am proud of the team, the players and how we showed our character today.
"It was difficult, it was a typical English cup game - long balls, battles, but a great performance from the lads and that is very positive."
It was a solid display from Saints that Ipswich counterpart Mick McCarthy could appreciate, even though that organisation and Long's first-half goal made it a "damp squib" of a cup replay.
"Of course it is disappointing for us all," he said
"Somebody said to me after (the home loss to Derby) Saturday 'oh, I am really disappointed' - well, we all are," the Town boss said.
"We did not want that game to be like that
We wanted it to be a rip-roaring cup tie
They didn't allow it to happen.
"We should give a bit of credit to them
It is not always us that is to blame - we have tried our hardest, as we always do, but they had a damn good side.
"I watched them beat Arsenal, I watched them beat Manchester United, you know, so it is no great shame on us that we have lost to Southampton.
"The shame is, I guess, or the pity, is that we didn't have the exciting cup tie we were all hoping for."
Source : PA