Lampard praises young midfielders
The 34-year-old, who scored the country's opening two goals, believes the impact and influence from the inexperienced pair was equal to that of a player beyond their years and that they were integral to England's control over the game.
"Tom played with such intelligence in midfield, he's a pleasure to play with and at such a young age he's going to be right in the middle of the team for many years to come," Lampard told the Football Association's official website.
"And Alex was brilliant. He lit up the first half with his injection of pace and running with the ball. It's great to see exciting young players like that playing for England."
Lampard did, however, concede that there is room for enhancement in the squad, which he hopes will be displayed during the second qualifier against Ukraine on Tuesday.
"We will try and improve," he said.
"Whenever we play, even if we play pretty well, we always look for areas to improve. I think we took our foot off the pedal at times in the second half, and maybe that's natural when you are 3-0 up with another game in a couple of days.
"But we need to keep a high level for 90 minutes on Tuesday and try to win against Ukraine."
Cleverley made his competitive debut for England - after a run-out against Italy in the August friendly - and the Manchester United man was humble with his post-match thoughts.
"The win is the most important thing and 5-0 away from home anywhere is a good result," he said.