The veteran netted a 50th-minute penalty after Emil Forsberg's fine opener on the stroke of half-time as the hosts briefly threatened to chalk up an imposing advantage, but then faded as the clock wound down.
Denmark substitute Nicolai Jorgensen netted from close range with 10 minutes remaining to make it 2-1, reducing the aggregate deficit ahead of the second leg in Copenhagen on Tuesday.
"After [taking] the 2-0 [lead] we dropped off. We were tired," Ibrahimovic was quoted as saying by Voetbal International.
"Before, I felt like we were more often able to score, but we lost control little by little.
"Then you get a goal against, but ultimately it's all about results. We won and that's what counts."
Ibrahimovic, who plays his football for Paris Saint-Germain, conceded that he found it difficult to prepare for the game against the backdrop of the terror attacks in the French capital on Friday.
According to the latest figures released by French officials, the attacks killed 129 people and critically injured a further 99.
The Friends Arena in Solna was illuminated in the colours of the French flag as a mark of respect on Saturday, and Sweden and Denmark observed a minute's silence before kick-off.
"I have tried to focus entirely on this game, but it was very difficult," Ibrahimovic said.
"It's tragic what happened there. This kind of thing should never happen."