Oxlade-Chamberlain, 18, made his first Premier League start in the match at the Emirates Stadium last Sunday and he assisted the Dutch forward for the hosts’ only goal.
Although the Gunners lost the tie 2-1, the ex-Feyenoord striker praised the former Southampton youngster for how well he played.
“Alex can be proud of giving a performance like that on his first Premier League start,” Van Persie told Arsenal’s official website on Friday.
“He moved nicely, worked hard, did good things on the ball and protected it well, which is particularly important against big teams.
“He can look back at a good game of football and we were all really pleased for him.”
Arsenal defender Yennaris, 18, came on for Johan Djourou at half-time for the Gunners and impressed with his marking of Old Trafford winger Nani.
“I’ve seen him improve his game massively of late, even over the last couple of weeks,” Van Persie revealed.
“What I like about him is that he always looks forward when he has the ball. He’s a right back who wants to play and bring others into the game – there aren’t many full backs who always do that, but for me it makes a massive difference.
“On top of that, you could see that Nani became less dangerous in the second half and Nico played a big part in that.
“Like Alex, he can be proud of himself; to play like that in such a big game shows great promise.”