England were relegated from the Nations League top tier this month after a six-match winless run, with Southgate drawing flak for their performances.
"I think it's in some parts harsh. And when I say some parts, it's something that we all sign up to in our own ways, and the England job is right up there for the pressure," Lampard told reporters ahead of Everton's league trip to Southampton.
"I'm not going to sit here and say that people can't criticise. I think if things are constructive and people have opinions, great.
"But once this World Cup comes in and, in the build-up to it, it'll be great if everyone can really get behind the team and Gareth ..."
Much of the criticism directed towards Southgate has focused on his "cautious" approach.
"I remember the fantastic French team that won the last World Cup without really playing beautiful football," said Lampard. "(In) modern-day football, there are lots of different styles and little ways to win a game.
"I think it would be absolutely Gareth's decision about how to approach an Iran or USA compared to how they approach another type of team further into the competition if we get there."
England begin their Group B World Cup campaign in Qatar against Iran on November 21st.
