Real Madrid took the lead through Karim Benzema, but Milan hit back through Ronaldinho just minutes later from the penalty spot.
“It was important [not to lose], we knew that it could be a very bad result – and if we had won that would have been great,” Alonso told Sky Sports News.
“Now we have a chance maybe to go through if Milan beat Marseille, but a draw is not bad at all.
“We were in control of the last quarter of the pitch, we have defended quite well but we haven’t been able to score and that is a shame as we could have won here.”