"We feel like there's not much pressure on us. We're playing some good stuff which is maybe externally building a little bit of pressure," Barclay told reporters.
"But within the group we're not getting carried away. England are playing well. You don't go that many games unbeaten without playing well," he said.
Scotland have beaten Ireland and Wales at home in this year’s Six Nations and lost narrowly away to France in a much-improved campaign.
"Expectations are there but we don't put any undue pressure on ourselves," said Barclay, who has replaced the injured Greig Laidlaw as captain.
"We kind of feel like the expectations are more on England. They have gone how many games unbeaten. We've only won two games this Six Nations.
“The fact is we're playing a Six Nations which is five games long and we're on game four," the 30-year-old flanker added.
"They are all big games and this is the next one. That is maybe a slightly boring response but that's the reality of it.
"You don't look at the following week, you look at England - they are too good a side to look any further."
England coach Eddie Jones said last week that Scotland were the side under pressure going into the game at Twickenham.
"Scotland are already talking it up," he said. "They've got belief, they've got confidence.
"Confidence leads to better performances and better performances lead to high expectation,” said Australian Jones, a master of pre-game hyperbole.
(Reporting by Mark Gleeson, editing by Ed Osmond; Editing by xx)
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