With away support banned by local authorities for the night, Maccabi went down 2-0 at Villa Park through goals from Donyell Malen and Ian Maatsen.
Afterwards, Lazetic said: "It was a 50-50 match, with few opportunities for either side, that was ultimately decided by the quality in the final third.
"It's always hard when you concede just before half-time but we started the second half well and had a good opportunity to score. We were up against one of the best teams in Europe and for the most part held our own."
Skipper Dor Peretz also said: "We're never going to be happy with a defeat. We defended really well but then came a high-quality first goal and we couldn't find a way back; it came down to the minor details in defence and in attack with our chances.
"We should take this experience into our next games; we performed well at a difficult place to come against a top team. We have to go away and work on the little things."
Peretz had two good chances on the night and added, "They were really good chances, but were denied by two really good saves, especially the second one. It's something I have to improve, to test myself more."