Moyes said: "Leverkusen have a good record of scoring late. We were aware of that.
"They did a great job but we played against a Champions League side and we're not quite at that level.
"We're still in the tie and we have half a chance in the second leg.
"We'd like to have played more attacking. The players did a brilliant job with the structure. We got done by two corner-kicks. The second one was really poor from our point of view.
"It's going to take some performance because they're a really good team. You never know what's going to happen. Let's try to get one and then see if we can get two. We'll pick ourselves up for next week and hopefully get the crowd behind us.
"This team we're playing will be Champions League next year. We have to recognise what we're playing against. We'll have to do exceptionally well to get that result."