It could have been worse for Saints, who trailed at St Mary’s after Darren Ambrose’s first-half header put the Championship club in front, but Morgan Schneiderlin equalised before half-time.
Despite dominating the second period, Koeman’s team were unable to find a winner and must now travel to Portman Road on Wednesday, January 14, in between Barclays Premier League trips to Manchester United and Newcastle.
“I don’t understand why you say congratulations, we have to play the replay and that wasn’t what I expected,” Koeman said.
“Am I annoyed? Of course, because we can’t make a lot of changes in the team and I don’t like to make changes. I believe in playing the strongest team.
“We chose not to play Toby Alderweireld today because of a risk to his hamstring but otherwise it was our strongest team.
“If I give out the message of making changes, the players can say afterwards, ‘the manager isn’t taking it seriously’.
“What happens now next week I don’t know. We have to play three away games, difficult ones, so we will see what happens.”
Saints began the tie as strong favourites, having secured a draw against Chelsea and a 2-0 win over Arsenal in their previous two league matches.
Ten points in four games has lifted Koeman’s side back into the top four but the Saints boss claimed he was fearful of Ipswich, who are currently second in the Championship.
“I was afraid for today’s game,” Koeman said. “There has been a lot of positive attention for everyone at the club after Chelsea and Arsenal and my experience is the next game is very difficult.
“Ipswich had an unbelievable spirit, 5,000 fans supporting the team and this game was their whole focus.
“I was afraid for today and the final result shows that because we didn’t start the game well.
“We started sloppy and you know that if you have to change that, it is very difficult.”
Koeman added: “If you put in 80 per cent and the opponent puts in 120 per cent, there is no difference between the Championship and Premier League.
“We knew that and that was shown in the first 20 minutes.”
Sadio Mane, who was on the scoresheet against the Gunners on New Year’s Day, missed the clash and has been ruled out for four to six weeks with a calf injury.
Southampton do not expect the midfielder to play in the African Cup of Nations although Koeman said he may travel to undergo tests with the Senegal medical team.