The two sides meet at the Metalist Stadium in Kharkiv on Thursday evening with the Ukrainian outfit having emerged from last week's trip to Tyneside with a creditable 0-0 draw to give them a slight advantage in the quest for a place in the last 16.
However, they were made to work hard for it - striker Papiss Cisse had two goals harshly disallowed for offside - and Markevich is expecting another tough game in the second leg.
Asked if Newcastle, who currently sit in 16th place in the Barclays Premier League, had passed up their best chance of progressing, he said: "No, I don't.
"I think it's level. Our chances to win are equal and our chances to go through are equal.
"As I said after the first game, Newcastle are a very good team and they shouldn't be in the position they are in. They should be in the top 10, minimum.
"We had a hard game in England, when we felt we lacked game practice, but everything will be decided tomorrow evening.
"The mood is great, the same as it was in England. Newcastle are a very good team. They are coming here with a full squad and we will see what happens."
Metalist ran out at St James' Park having not played a competitive match since December 6, when they lost 1-0 to Rapid Vienna in Austria in their final Group K fixture.
But Markevich is confident there is more to come from his team.
He said: "This is simple: You all know that Metalist can play better and we hope we will."
Any Metalist victory would send them through, while a score draw would be good enough for Alan Pardew's men to progress.
In the circumstances, an away goal could prove crucial, but Markevich insisted he was not attempting to second-guess what approach Pardew would take.
He said: "It's hard for me to say, it's more a question for the opposition coach. Newcastle will play as we allow them and we will play as they allow us.
"It depends on the opponent, but usually we choose an offensive style of game and we will try to do that."
The game will be played in front of a large and passionate crowd - tickets sales had exceeded 38,000 by this afternoon and is fast-approaching a 40,000 sell-out - and Markevich is promising Newcastle and their fans a lively welcome.
He said: "It will be a great atmosphere. It will be like in England because English fans also know their football and also know how to support.
"Our fans support very well and are very passionate, and I think tomorrow you will like the game very much."