England chased down 277 despite once being 117/5 in the final innings in Manchester.
The skipper reserved special praise for the sixth-wicket duo of Jos Buttler (75) and Chris Woakes (84*), who took England out of trouble waters and paved way for a mighty impressive three-wicket win.
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None of it would've been possible, of course, if England hadn't come back strongly with the ball in the third innings after conceding a 107-run lead at the end of the first half.
Dismissed for 219 in response to Pakistan's 326, the hosts dislodged the visitors for just 169, ensuring they weren't out of the game at the start of the chase itself.
"We knew it would take something special but after last summer (pointed towards the Ashes chase in Headingley) it is very hard to stop believing. It’s a real strong trait of ours," Root told reporters.
“It was a brilliant chase. I couldn’t be more proud of the lads. Jos, it shows the mental strength, to play that situation and manage different passages of it, calculating risks, manipulating the spinner, brilliant innings, and Chris was magnificent too."
"The more important thing is we back it up again, and keep learning, but the clarity with which they played shows the maturity of the group too," he added.
In the chase, Woakes said as he went out to bat and joined Buttler, the communication was to take the game back to the opposition and not let the difficulty of the situation play into their minds.
"It was a good idea to take them on and put them under pressure," he said, before adding in praise of his partner that "He (Buttler) is one of the best white-ball players in the world – one of the best run-chasers – and he showed why today."
Pakistan captain Azhar Ali conceded that the Buttler-Woakes duo was able to put the pressure back to his team.
"When Buttler and Woakes came in and played their shots, they put us under pressure and we couldn’t really answer them," Azhar said.
"So credit to them, they outplayed us in that period. Maybe we were too late to bring fielders up."
"It’s disappointing but not over yet, there are still two tests to go," he added.
The next Test begins on August 13 in Southampton.
(Inputs from Reuters)