Wilkinson acted decisively at half-time as McAteer and Morgan were replaced by Rachel Rowe and Kayleigh Barton, but Wales lacked the fluidity they showed in their opening two Euro qualifiers.
Most of Wales’ players are now in their off-season but despite lacking rhythm Wales did not lack endeavour and their efforts were rewarded on 64 minutes when they equalised from the penalty spot.
Rowe’s decisive run caused panic in the Ukraine defence and after Keliushyk saved James’ effort, Ceri Holland’s firmly struck drive was handled by Olha Basanska, with Barton firing home the penalty.
Barton glanced a header just wide as Wales pushed for a winning goal, but there was a lack of composure about the hosts, every pass was hurried and despite masses of pressure, a winning goal proved elusive.
Fishlock’s trickery saw her slalom into the penalty area on 88 minutes, but Keliushyk saved her effort at the near post.
Rowe also came close in stoppage time as she flashed a shot across goal from long-range, while Holland also fired wide as Ukraine held on.
Wales boss Rhian Wilkinson told BBC Sport Wales:
"I think I would be lying if I said it wasn't a frustrating match, we are better than letting one mistake cost us two points.
"I thought we lost our way in the first 45 minutes but I was proud with the way the team responded.
"We stuck with the process and the things we are trying to implement.
"Ukraine is a country who have been through it all. We were always going to have to earn everything we got and while we didn't do that in the first-half, we did in the second."