Luiz Adriano opened the scoring on 37 minutes before a goal from Alex Teixeira and Douglas Costa's brace in the second half set up the big UEFA Champions League win at Donbass Arena.
With Bayer Leverkusen thrashed 5-0 by Manchester United, Shakhtar moved into second in Group A with a match remaining.
But Lucescu said his side were fortunate to claim three points despite the comfortable-looking scoreline.
"As we expected, the game was hard, especially in the first half. In the first 15 minutes they had the advantage as they totally controlled the ball," the veteran Romanian coach said.
"I think we surprised them with some fast and clever play after the corner that led to Luiz Adriano's goal.
"At the end of the first half they put lots of pressure on our defence. They had some good opportunities and I must admit we were lucky as they failed to take their chances."
Teixeira's goal, three minutes into the second half, allowed Shakhtar to punish an attacking Real Sociedad side on the break.
Lucescu said it was that effort which put the result beyond doubt and made it easy for his side.
"The key moment was Alex Teixeira's goal, when we pressed successfully. Once it became 2-0, Real understood they wouldn't get anything here," Lucescu said.
"We controlled the ball well, put together a lot of combinations but the outcome was practically settled.
"Real started to play open football, which enabled us to utilise our counter-attacks. The last part of the game was quite simple for my players."
Lucescu has challenged his team to claim a win against Manchester United at Old Trafford on the final matchday and reach the knockout stages.
"We have two weeks to prepare for the game at Old Trafford," he said.
"We have only one option: we need to defeat Manchester United. We will do everything possible to achieve this."
