Southampton had 21 attempts at goal, nine of which were on target with their opponents pale in comparison with just six attempts at goal, two of which were on target.
"We know it's not the best result that we expect, but we still have one game to play and we will go for it, that's for sure," Koeman told the club website.
"I'm not happy about the final result. I'm more happy about the second half. We played more direct, more aggressive and finally we had five or six very good chances to score.
"We saw that we are the better team and we had the better chances, but we have to be more clinical," the 52-year-old added.
Midtjylland midfielder Tim Sparv opened the scoring at the stroke of half-time but Southampton clawed their way back into the game with Jay Rodriguez scoring from a penalty in the 56th minute.
"They frustrated us at times but that's all part of the Europa League. You back us to score and keep it tight. I'm sure we will do in the second leg," said Rodriguez, who scored his first goal since March 2014.
"We created enough chances to get the win but it is still all to play for and we've got another leg to go."
The Saints also had a goal disallowed for a foul by defender Steven Caulker after the loan signing put the ball in the back of the net from a James Ward-Prowse corner.
"I think the goal should stand. I couldn't believe he gave a foul against me to be honest. It was a bit of a shock," Caulker said.
"But we were a lot better in the second half. The gaffer had a strong few words at half time about playing more direct. I thought we did that and caused them a lot of problems," the 23-year-old England international added.
(Reporting by Shravanth Vijayakumar in Bengaluru)
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