Despite winning their opening match on Monday, Southgate is already wanting his team to be concentrating on their next World Cup match against the central American side on Sunday.
The Three Lions managed to beat their previous opponents 2-1, with a double from captain Harry Kane, but Southgate had his players back in training on Tuesday after their return to their Saint Petersburg base at 6 a.m on Tuesday morning.
"There are always things (to improve),' the England manager said.
"We are a team that are improving and developing, and therefore there will always be things that we can get better at.
"We're a long way from perfection. What pleased me is that there has been a long period of work gone into (Monday's) result from all the players and all of the support team.
"If you don't get the win, even though you've done so many things right, that can breed a little bit of doubt."
The former England defender is happy with the outcome of the Tunisia game, but is insistent that his players not rest on their laurels.
England's players lack little experience at major tournaments, with 9 players making their World Cup debuts in Monday's match. Regardless, the manager has plenty of experience from his playing days and during his time as England U-21 coach to know how best to treat tournament football.
"We have to prepare as perfectly for Panama to make sure we get the result in that game we need.
"I think the players know it's hard to win a match in the World Cup against any opposition and Tunisia were opposition we respected."