The England coach picked a strong team and was rewarded with an impressive first-half performance and goals from Kane and Cahill.
"We were deservedly a couple of goals to the good at half-time. Far more good situations than in recent games", he said.
Lingard was unable to connect to a Tripper ball from the right and after a superb save from Uzoho to deny Sterling, who was again in on goal on 38 minutes but fired over - the Manchester City man set up Kane for England's second. But after that we dealt with it well.
Gareth Southgate's charges were comfortable on the ball and were using the pace of Sterling up front while Gernot Rohr's men were disorganised and gave England too much respect. It was a decent exercise for us to adjust to that.
'Some slightly better decision making or quality and we would have scored more'.
Looks Like WONDER WOMAN 2 is Headed For The '80s
It grossed more than 821 million dollars on a budget of 149 million dollars, breaking records for a female-directed movie. Jenkins said she believes superheroes like Wonder Woman become the "fantasy embodiment of ourselves".
England made a sharp start to the match, but their first opening arrived in controversial fashion when the referee refused to stop play after two Nigerian players had clashed heads, instead awarding England a free kick in a good position seconds later.
"I don't think we got a lot of answers today though because Nigeria just lied down in the first period and let England do what they want".
England play their final warm-up game against Costa Rica at Elland Road, Leeds on Thursday, 7 June.
England-based Victor Moses, Iwobi and Aina are all in contention to start while Odion Ighalo, John Mikel Obi and Ahmed Musa are also expected to play some part at the 82 000-capacity arena which Alli usually lords over in Tottenham Hotspur colours.
Their first World Cup group game is against Tunisia in Volgograd.