Both Root and Jos Buttler scored hundreds but Pakistan still managed to end a run of 11 straight losses in completed ODIs with a well-deserved win.
Root now expects England to bounce back strongly against Bangladesh in Cardiff on Saturday.
"The most important thing now for us as a group is not to panic," he told reporters.
"We know what works for us as a formula, and as a team, but other sides are allowed to play well and we've got to make sure we learn quickly and bounce back at Cardiff.
"The temptation is to get a little bit tense, but one of our great strengths as a side is sticking to the way we go about things and be as smart as possible.
"And the beauty of this format is I do believe the best four teams over the tournament will qualify for the semi-finals and we've got to make sure we play some good cricket in our remaining games."
The Test captain insisted: "One thing this side doesn't do very often is to make the same mistake twice and I'm sure the guys will make sure it's a very different performance against Bangladesh."
It was all so different from England's fine fielding effort during a 104-run thrashing of South Africa in last week's first match of this World Cup.
"It was just a really bad day in the field," said England captain Eoin Morgan.
"There were mistakes that we don't normally make. And that's disappointing.
"We've gone from probably one of our best performances in the field at the Oval to, not extremely bad, but it's cost us probably 15-20 runs in the field which is a lot in the one-day game."
The umpires warned both Morgan and Pakistan counterpart Sarfaraz Ahmed about deliberately throwing the ball in on the bounce.
Buttler also appeared to look long and hard at the ball after his dismissal.
"There were discussions throughout the whole of the two innings," said Morgan.
"The umpires came to me mid-innings and seemed to think that we were throwing the ball in on the bounce too much or it was being over-exaggerated.
"They emphasised it would be the same for both (teams).
"The conversations that were stopping the game were that Pakistan were doing the same thing," he explained.