Goals from Kyle Glasgow and Coben Fergusson in a narrow 3-2 defeat leaves the tie in the balance ahead of the return leg at Forthbank Stadium next week.
Speaking to RangersTV after the game, Smith reflected: “It was a really difficult start.
“[The first goal] we probably can’t do anything about.
“It takes a horrible deflection, and then for the next 15 minutes I felt like we struggled in the game.
“We knew they would be a difficult team, good technically and physically, so we took 25 minutes to get up to speed.
“Once we did that and got some control in the game I felt we were really good and were threatening their goal.
“I thought we were by miles the better team in the second half.
“Dynamo Kyiv were in a situation where they were 2-0 up and didn’t know whether to stick or twist.
“Their goalkeeper made an error and we continue to play the way we were.
“It was a man-for-man game so it was a big ask for our players, and if you’re going to play man-for-man you’re bound to leave some spaces and we needed our goalkeeper to help us at certain points.
“My biggest disappointment was the timing of the goals.
“It’s really difficult when you score and concede straight away, but fair play to the players.
“They kept pushing, subs had an impact, and we’re still in the tie with all to play for next week.”
The Ukrainian outfit will make the trip to Scotland in seven days time.
They showed their quality in abundance with their three goals, and although Smith is well aware of the task ahead, he admits his side can take encouragement from today’s showing.
He added: “We deserved the goal at the end to keep the game in the balance.
“Overall, in terms of our quality and intensity, I thought we were the better side from about the 25th minute, but we do know from watching them that they have real threats.
“We’re still going to need to deal with that next week but play our game too.”
