Robert Lewandowski and Marcel Schmelzer struck on either side of a Cristiano Ronaldo goal to hand Dortmund the win to go top of Group D.
Alsonso felt that the result was harsh on Real Madrid, who proved to be formidable opponents and tested Dortmund on several occasions.
"Both teams had chances to win the match. I think a draw would probably have been a fair result, but Dortmund worked very hard to their win," Alonso told Uefa.com.
"They played very well at both ends of the pitch and got that little bit of luck for their second goal. We came here expecting an even contest. Dortmund have enjoyed a lot of success in Germany over the past couple of seasons."
Real Madrid are now second in the group with six points, a point behind Dortmund and Alonso feels that there is still everything to play for in the competition.
"We've lost tonight, but there's still everything to play for in this group. We lost against a very good opponent in front of an amazing crowd and that just gives us more motivation to win the next match."
The return match at Santiago Bernabeu will take place a fortnight from now on 7 November.