After taking a wicket with the first ball of the Test, England dominated Pakistan across two and a half rain-affected days.
They appeared more measured in their approach than during the ultra-aggressive Stokes-McCullum regime, but still scored at 4.55 runs per over – albeit against a poor Pakistan side.
“We played to the fashion that we wanted to,” Trescothick said.
“We wanted to be able to be clever and smart. There’s moments within the game we’ve done that brilliantly.
“We still have that mantra of applying pressure because that’s the best way of being dominant over teams, if you can put them under pressure.
“I did enjoy the fact we were still scoring quite quickly especially when the ball was new.”
New Zealander Stephen Fleming has been appointed as McCullum’s replacement but will not take charge until the winter tour of South Africa, leaving Trescothick as interim.
Fleming was in contact with Root and Trescothick “every day” during the win over Pakistan.
“He was adamant me and Joe take it on and just run with what we feel is right, to try and get the group back in shape, with a few pointers on what he wanted and how he could see his style being implemented within the group,” Trescothick said.
Trescothick has worked with England as a batting and assistant coach since 2021, but former Australia coach Mike Hussey has been approached by Fleming to be batting coach when he takes over.
Hussey worked with England under Michael Mott during their 2022 T20 World Cup win and with Fleming at Chennai Super Kings in the Indian Premier League.
Trescothick could move to a white-ball only role, where McCullum remains England coach, but said he would “love” to stay on with the Test side.
“I want to be involved in all formats of the game because it’s a wonderful place to be,” he said.
“Working with the best and seeing England cricketers do well.
“That’s not really for me to judge so I’ll wait and see what happens.”