Kenny's side sit third in Group B1 having taken just four points from as many games
Republic of Ireland boss Stephen Kenny said he was "disappointed" and "frustrated" after his side failed to close out the game against Ukraine.
After beating Scotland, Nathan Collins' superb individual effort gave the Republic the chance to secure back-to-back Nations League wins.
However, Artem Dovbyk's goal earned Ukraine a draw.
"Having taken the lead we wanted to go on and win it. We had a lot of play in better areas than they had," he said.
Speaking to RTE, Kenny added: "I'd have to see the goal we conceded again, it looked like we were a bit wide open and we shouldn't have been. It's not a goal we should have conceded.
"They were a threat on the left wing with the underlaps of [Mykhaylo] Mudryk, he's very quick, but we defended our box fine, they didn't really have clear-cut chances.
"We had a lot of the ball so I'm a little disappointed we didn't go on and win it, but Ukraine are a quality team, they are real quality.
"The players' attitude was brilliant, I can't praise them highly enough. We're just kicking ourselves a bit that we haven't got more points this week."
Kenny praises 'exceptional' Collins after wonder goal
While the Republic demonstrated signs of the confidence gained from Saturday's 3-0 win over Scotland in Dublin, Collins' outstanding 31st-minute solo effort was undoubtedly the highlight for Kenny's side in Lodz.
Collins, who made his international debut as a late substitute in October's friendly win over Qatar, has established himself in Kenny's team having played every minute of the gruelling four-game window.
"Nathan has been really, really good," Kenny said of the 21-year-old Burnley defender.
"His decision-making is excellent and he's been exceptional over the four games. We have players coming back in so we have more options now and we need that competition for places going forward to raise the standard."
Kenny added: "While I thought it was a good performance, I do feel we can be much better again and I want us to be. I'm just a bit frustrated that we couldn't be a bit better and win that game.
"But I couldn't fault the players, they were brilliant. It's just something that we have to continue to improve.
"I have no right to feel disappointed. The support has been amazing and we feel that, we're just a bit frustrated that we didn't win this game."
