Both players were included in the starting line-up for the World Cup 2014 qualifier in Chisinau on Friday and could feature again against Ukraine at Wembley on Tuesday.
Lampard and Milner also played in the comprehensive opening win and the former felt that coach Roy Hodgson had got the balance right between youth and experience.
"It feels like there's a nice blend [of youth and experience] on and off the pitch," Lampard told reporters.
|7/1||Tom Cleverley is 7/1 with William Hill to score the first goal in England v Ukraine
"It was a great performance [from Oxlade-Chamberlain], his pace and ability on the ball and the confidence he has in him – it's not easy to step straight into an England team – is great to see. It gives us all a bit of a smile to see a young boy come in and play with that about him.
"We all need reminders from the manager or a little bit of help in a certain way but as a youngster, even more so. We've got a great manager with experience to be able to give him the reminders that he needs and encourage him in the right areas."
Milner, meanwhile, was keen not to play down the influence of the senior players in the squad after Lampard scored twice to send England on their way at the Zimbru Stadium.
"We're blessed to have the experienced players with the amount of caps they've got," he said.
"They're still at the top of their game and there's younger players coming in, who I've played with at Under-21 level, and even younger lads such as Alex Oxlade-Chamberlain step straight in and don't look fazed at all. There's a good mix at the moment and that's a positive thing to have.
"The experience he [Oxlade-Chamberlain]'s gained at a major tournament already, at such a young age, is invaluable really and the more games he plays the better he'll get. He's another good player who's learning and we've seen what he can do already, so think how good he'll be in a few years.
"Cleverley is a top player, he's very comfortable on the ball, gets in great pockets in the position he played the other night and he's a good link between the midfield and forwards but also does his work defensively as well to keep the shape.
"If the lads behind him want to bomb on they've got that rotation in the midfield which is important. He's done a great job for the team."