An Emil Forsberg goal and Zlatan Ibrahimovic penalty either side of half-time at the Friends Arena in Solna put the hosts in control in Solna.
But Nicolai Jorgensen got on the scoresheet with 10 minutes remaining to see Denmark having netted a vital away goal heading into Tuesday's second leg in Copenhagen.
And Bendtner, who played the full game, was pleased with how his side reacted to remain very much in the tie.
"We talked at half-time that we had to go out and do better for the second half," he was quoted as saying by Fyens.
"So it is obviously negative, they got a penalty, but the positive is that we scored so we were in the game."
Bendtner urged his team to maintain possession better in Copenhagen, saying they looked dangerous at times in the first leg.
"In the periods where we played ball, we did well," he continued. "But we did not do it enough."