Anderson, 38, is 10 Test wickets away from the rare 600-wicket milestone, but struggled in the opening Test of the series against Pakistan at Old Trafford, finishing with match figures of 1-97 as England won by three wickets.
The English have rotated their attack all summer, given the challenge of playing six Tests in six weeks on the bowlers, but Anderson has survived the cut for the Second Test which starts on Thursday.
“It would be very silly for us to write someone like Jimmy off,” Root said.
“To question Jimmy’s ability and his record - do that at your own peril.
“There’s a reason he’s got so many wickets over such a long period of time: it’s because he’s a consistent performer.
“I don’t think it’ll be long until he’s back in the wickets big time.”
England’s XI is further complicated by the fact all-rounder Ben Stokes will miss the remainder of the series for personal reasons, meaning they’ll need to add batting depth to the middle order but reinforce the bowling line-up.
While Anderson struggled for impact in the First Test, Chris Woakes was named Player of the Match after scoring a decisive final innings 84no and taking four wickets.
Veteran Stuart Broad took six wickets for the match, while Jofra Archer claimed four and spinner Dom Bess took two.
The expectation is that Archer will make way for Mark Wood, while specialist batsman Zak Crawley will replace Stokes and bat first drop.
Meanwhile, Pakistan have made their intentions clear, declaring they want to “cash in” on Stokes’ absence having come close to winning the First Test.
Pakistan coach Waqar Younis: If hes not around England will probably be a touch light in their middle order, so were going to talk about that and try to cash in.
Hes the kind of batsman who takes the game away from you single-handedly at times. But the way we bowled at him in the previous game showed we had very clear plans and executed really well.