The Three Lions failed to break Italy down thereby dropping to the bottom of the group.
England lost 1-0 to Hungary in their first group game before drawing 1-1 with Italy on Tuesday.
It has been suggested that Southgate is failing to get the best out of England's attacking players as he favours a conservative approach.
England have not scored a goal from open play in their first three fixtures, with Harry Kane's goal against Germany coming from the penalty spot.
Maguire maintains he has confidence in Southgate and has pointed to his record at the 2018 FIFA World Cup and EURO 2020 as evidence.
"[Southgate's] record over the last four years speaks for itself," Maguire told BBC Radio 5 Live.
"When you play at the highest level there's pressure and scrutiny and criticism, and every game that you don't win there will always be criticism [afterwards].
"The last few games we haven't scored enough goals, but we got to a World Cup semi-final playing this way and we were a penalty shoot-out away from winning the Euros in our home country, which would've been one of the greatest moments this country has ever seen."
"Let the football do the talking. Everyone get behind us for the World Cup and keep pushing us, we're doing our best to improve," he continued.
"We've shown there's still areas to improve and if we want to lift the World Cup we have to strive to improve.
"Every day that we're together we have to aim for that because we want to set high standards and the next [aim] is to lift the trophy."
England will play USA, Iran and Wales in the group stages of the Qatar 2022 World Cup later this year.
