Anderson took five for just 73 runs as he bowled 13 successive overs on Sunday morning at Trent Bridge to limit Australia to 296, leaving the tourists short of England’s tally of 309.
And Cook hailed the man-of-the-match for his telling contribution after Anderson ousted Brad Haddin (71), aided by a DRS referral, to secure an opening win.
“Australia fought incredibly hard and a lot of credit to them for the way those guys batted today, but we just hung in there incredibly well,” Cook said.
“Jimmy was outstanding. He always wants one more over – I think 13 was probably quite a lot in that first hour!”
Cook also rubbished claims that England are overly reliant on Anderson, pointing to the performances of Stuart Broad and Steven Finn.
“No, not at all. He’s a world-class bowler and you sometimes use him in these situations when you know there’s a timeframe. He had an amazing rhythm in this game.
“But [Stuart] Broad and [Steven] Finn have done outstandingly well for us over a huge amount of time, but it just happened to be Jimmy’s day and Jimmy’s game. Sometimes it happens like that.”