Pakistan have gone winless in 10 home Tests since February 2021, the latest humiliation being swept 2-0 by Bangladesh earlier this month.
They also lost 3-0 in Australia earlier this year.
"It's not acceptable for Pakistan to not win a home Test for that long and we accept the responsibility for that," said Masood at a press conference in Karachi.
"As a cricketing nation we all are hurt right now."
Masood was confident that batting great Azam would soon be back to his best after managing just 64 runs in the two Bangladesh Tests.
"We all know Babar is one of the top batters in the world and despite not scoring big runs the good thing is that he is not out of form, we have to back him," said Masood.
Azam has not passed fifty in Tests in 16 innings dating back to December 2022.
England arrive in Pakistan on October 2 with the first Test starting in Multan five days later.
The second Test is also in Multan from October 15 while the final match is in Rawalpindi from October 24.
"I assure you that everyone is eager to stage a comeback in this series and take Pakistan cricket in a good direction," said Masood.
England swept the series 3-0 when they last visited Pakistan in 2022.
"For me, pressure is a thing of privilege because leading your country is a great honour but with it comes responsibility," said Masood, whose captaincy tenure runs until May 2025.
"If results are good then I will serve, if not then I will be punished. I don't run away from challenges and this coming series is also very challenging."