Cook hails Anderson for his extra workload given the 'time frame' and which ensured a valiant 10-wicket stand proved too late in a 14-run dramatic result at Trent Bridge.
England beat Australia to win the first Ashes Test in nick of time
Anderson showed admirable stamina as he bowled 13 successive overs on the final morning, his burst of three wickets for six runs helping to give him 10 in the match, including the final wicket of the match as he had Brad Haddin caught behind after England had referred the decision to the third umpire.
"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 at the post-match presentation.
"Jimmy was outstanding. He always wants one more over - I think 13 was probably quite a lot in that first hour!"
Asked if there was an over-reliance on Anderson, Cook said: "No, not at all. He's a world-class bowler and you sometimes use him in these situations when you know there's a time frame. He had an amazing rhythm in this game."
Anderson ended the contest with match figures of 10 for 158, and asked if it had been his best performance in an England shirt, he told Sky Sports: "Yeah I'd say so.
"We knew it wasn't going to be easy at the start of the day, but I thought the lads stuck to it and stayed calm when it was getting tough. I'm just delighted to get the win."
Australia captain Michael Clarke, meanwhile, was proud of his players for their contribution to a memorable Test encounter.
"The boys can hold their heads high," he said. "It was a wonderful game of cricket but credit to England.
"They fought really hard through the five days and the two best performers were Ian Bell making a hundred and Jimmy Anderson getting five in both innings, so they deserved to win."
Ashton Agar's 98 on his Test debut was an obvious highlight for the Australians and one that bodes well for the rest of the series, and Clarke had special praise for the 19-year-old.
"He's played really well," he said. "He's an amazing talent, a great kid. He's got a very smart mind. He's a lot older than his age would tell you."
Reflecting on the rest of the series, which continues at Lord's on Thursday, he added: "I'm as confident as I was when we landed here.
"We get another crack in four days so we'll look forward to that."
Australia 291 for nine at lunch After what had transpired over four days, it was no surprise that there was plenty of drama ahead. While the combination of Alastair Cook catching and James Anderson bowling accounted for three of the four wickets needed, last pairing Brad Haddin and James Pattinson began striking boundaries, making England's fans nervous. Haddin struck 15 off one Steven Finn over as the target slipped down to only 20 needed at lunch break.
Australia 296 all out The tension was high now for both sides with Australia up against the refreshed bowlers as the scoreboard moved along. But the impressive Haddin was given out by third umpire Marais Erasmus after nicking an Anderson delivery to ensure Australia's brave run chase fell just short.
- Graham Caygill
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