Gary Cahill headed the hosts in front from a corner-kick, before Harry Kane made it 2-0 ahead of the half-time.
Arsenal’s Alex Iwobi pulled one back for Nigeria in the second half, as Rohr’s men improved greatly after the break.
“Clearly it was a game of two halves. I made four changes and change in formation also made a big difference.
“Travelling and preparation was not good enough,” he told reporters after the game.
Nigeria’s final friendly game before the 2018 World Cup will be against Czech Republic on Wednesday in Vienna, Austria.