The Scottish champions struggled to contain the Kazakh outfit's counter-attacking at the Astana Arena and face an uphill task for the home leg.
"It's a disappointing result, but we should have scored and it would have put a different complexion on the tie," said Lennon.
"But we're not down and out yet."
A 17th-minute opener from Andrei Finonchenko and a second-half header from Sergey Khizhnichenko made for a miserable night in Kazakhstan for Lennon's side, although Kris Commons struck the bar and Georgios Samaras headed wide as the visitors chased an all-important away goal.
Despite the defeat, the Celtic boss believes the way Shakhter played was not unexpected and it will be up to his players to make the difference in the second leg in Glasgow.
"It's not over," said Lennon. "We'll go back to Celtic Park and there's plenty there for me to chew on in terms of chances, but Shakhter didn't surprise us with the way they played. We knew they would throw balls forward - we should have dealt with the first one a bit better.
"I don't know how many chances we had - clear-cut ones as well - if you don't take your chances you make life difficult for yourself."
Lennon also admits improvement in terms of some of the individual displays will be necessary at Celtic Park and dismissed the recent loss of key players, such as Victor Wanyama, Gary Hooper and Kelvin Wilson as having contributed to the result.
"There's a few players who will be disappointed with their performances, and they've got to get better very quickly," added Lennon.
"I didn't really feel uncomfortable in the game at all. I thought we would score and that would put a totally different complexion on the tie, but the fact that we didn't just makes it a little bit more difficult now.
"Possibly, I think I've still got enough in the squad to come through the tie, so that's what we'll endeavour to do."
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