He said his third goal, which came from a Ruben Loftus-Cheek shot that deflected off the English captain´s heel into the net, "was one of the luckiest of my career".
John Stones opened the scoring with a brilliant header, before captain Harry Kane doubled the Three Lions' lead from the spot with a wicked penalty. England's previous high for goals in a World Cup match was set in its 4-2 victory over Germany in 1966 final.
It left the shell-shocked Central Americans out of their debut tournament with nine goals conceded in Group G. Tunisia were also eliminated. Kane scored another penalty just before halftime. Not many players get to score a hat-trick in the World Cup.
Current World Cup top scorer on five goals after two games, Kane was then substituted for Jaime Vardy up front, to a standing ovation from the almost 2,500 England fans at Nizhny Novgorod.
England's emphatic win over Panama was a joy to behold for England fans.
Get thee home from thy place of worship quick sharp as England are up first in World Cup action.
And they're well on their way to doing that at half-time against Panama.
Kane's hat-trick is the 52nd in World Cup history, and the second of this tournament after Cristiano Ronaldo, who achieved the feat in Portugal's 3-3 draw against Spain.
Southgate's task now will be to keep his young charges' feet on the ground, and guard against complacency whomever they face next from Group H's quartet of Japan, Senegal, Poland and Colombia.