The two sides meet at Wembley on Tuesday evening in a World Cup qualifier following England's 1-0 victory over the co-hosts at this summer's European Championships.
Wayne Rooney's goal was the difference in Donetsk with Ukraine left aggrieved by a refereeing decision that arguably cost them a point.
Marko Devic's shot crossed the line before it was scrambled away by John Terry but the assistant referee maintained the Chelsea defender had cleared the ball in time.
Milner reckons the England squad is much better prepared this time around as manager Roy Hodgson has had a chance to implement more of his ideas following his appointment in May.
Hodgson's first qualifier ended in a 5-0 win in Moldova on Friday, and Milner said: "We changed manager just before the tournament, and I think we looked very solid and difficult to beat but maybe didn't play as well as we could do with the ball.
"We are moving forward already, we saw that the other night. And the longer we are together working with the manager we will become better as individual players and as a team."
The 26-year-old has featured in every fixture since Hodgson replaced Fabio Capello and admitted he now feels like a more important member of the squad.
"I think I definitely feel more comfortable," he said.
"I have played a number of times and I think the more you are in and around the squad the more comfortable you'll be.
"I was very fortunate to get a number of caps at Under-21 level and I think the more experience you have at international level can only be a good thing for you as a player."
Despite his recent run of games, the Manchester City midfielder's goal in the win over Moldova was his first at senior international level.
Milner was pleased to open his account for his country, saying: "There is no better feeling than scoring a goal - the best thing is pulling on an England shirt and being part of a winning team.
"Everyone likes to represent their country and contribute to an England win, which we can get by keep improving and moving forward as a team - that is the most important thing."
Hodgson's side rolled over Moldova despite being without both Rooney and Andy Carroll through injury.
But with Frank Lampard scoring twice and Leighton Baines also netting his maiden England goal, Milner is pleased that the team are not overly reliant on their strikers.
"The more goals you have in your side, the more likely you are to win football matches," he said.
"If there is a lot of pressure of your striker - your Jermain Defoe, your Wayne Rooney or your Danny Welbeck - you need someone else to pop up with a goal and it is important we have that.
"I suppose it is pleasing the other night that a number of names got on the scoresheet and hopefully we can carry that forward - the more threats you have from all over the field, whether that's from set-pieces or in open-play, it is important for the team."
Milner collected a Barclays Premier League winners' medal with City last season and is a firm believer that playing with world-class talent at the Etihad Stadium has helped his own game progress.
"I don't think it'll do you any harm, winning titles," he said.
"As individuals you have success and you always grow up by winning the league, and the confidence you gain from that gives you the hunger to want to do it again.
"I'm very lucky to be playing with some of the best players in the world, you have to enjoy that and also learn as much as you can from training with these guys every day - it can only make you a better player yourself."