The goal was a jolt to Wales who would have expected to pick up from where they left off in their opening qualifiers, but they did produce several good chances to equalise in an engaging first period.
Twice Wales managed to find a pass that bisected the Ukrainian defence, but Jess Fishlock saw her shot blocked and Ceri Holland’s cross flashed across goal without a decisive touch.
Fishlock also saw a firmly struck left-footed effort tipped over the crossbar by Daria Keliushyk as the home side enjoyed over 75% possession before the interval.
Fishlock, who was awarded a special cap pre-match to commemorate her 150th appearance, might have levelled on 41 minutes but saw her volley – which she had to snatch at in a crowded penalty area - drift over the crossbar.
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."