Kaunas, however, were bright and on their toes and looked every bit the side that sits top of the Lithuanian league after 15 matches.
Smith admitted: "There is no excuse really for us. With the importance of the fixture, I thought we would have started brighter.
"I felt we started the game slowly and I thought there would be a bit more pace and passing of the ball.
"But credit to Kaunas, they defended well throughout the evening. Just before half-time was our best spell in the game and we had a couple of clear-cut opportunities that we might have done better with."
Rangers midfielder Kevin Thomson said he was confident of victory in the return leg in Lithuania next Tuesday.
"From what we saw in this game, I am sure we can improve and go to Lithuania and score an away goal," he said.
Thomson says Rangers can win in Lithuania next Tuesday
"The onus is going to be on them. It's always difficult being the team playing at home, when you have to dictate and try to score.
"Over there, we can try to employ the same tactics as last year, sit a wee bit tighter and try to use our pace up front to score on the counter-attack."
Kaunas manager Jose Couceiro believes his side are still the underdogs.
"I thought Rangers were the favourites and, after this first match, I still think they are," he said.
"I thought Rangers would cause us more problems but the second leg could be decided in the last 20 minutes and a team who have experience are, of course, at an advantage.
"This was a very good result but it's not finished."
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