"I think if you look at recent history we've been doing that," Cook said of the slow starts. "But we do now need to start looking forward rather than worrying about what happened ... and dust ourselves off and come back fighting."
Cook said the comeback series win in India, its first in almost three decades, was all the motivation his England squad needed.
"In Ahmedabad everyone was looking at us and wondering how we could play cricket and we bounced back and won an amazing series," he said. "I think the first thing we've got to do is remember we're a very good side and there's some very good players in that dressing room.
"We've had a bad game and we can hold our hands up and say that. We've got 10 days to go away now, we'll stay strong as a unit, and we'll come back fighting."
England had an interrupted preparation for the series, with two of the three tour matches affected by rain. There was also injury concerns over wicketkeeper Matt Prior, and doubt over which seamer would support Stuart Broad and Jimmy Anderson. Chris Tremlett got the pace bowling spot but didn't have a great impact, while Anderson only picked up two wickets in a below-par performance. Stuart Broad was outstanding with the ball in both innings, picking up 6-81 in the first. Cook's 65 in the second stand was the only innings of substance by an England batsman.
Jonathan Trott has struggled against the short ball in recent months, including both innings in Brisbane. The way he got out to Johnson in the second innings even came in for extra criticism from Australian opener David Warner, who told a post-match news conference it was "weak" and accused the England batsmen of having "scared eyes."
Cook criticized the timing and style of Warner's comments, and is backing Trott to fight back.
"He's had a tough game, he knows that," Cook said. "You have to remember that the guy's class though. He's had a little blip now in these couple of games but he's a class player and class players bounce back.
"We've been found short with the bat and we're going to have to go away and work on it."
Johnson has had his struggles against England, and wasn't even selected for the last Ashes tour for Australia, but has caused the English batsmen trouble on pacey pitches. The Australian paceman has vowed to keep up the short-pitch bowling in this series because "it's working," but wouldn't buy into the Warner-Trott conversation.
Cook said his batsmen would figure out a way to play Johnson.
"He's bowled very well in this test match and he bowled very well in Perth last time. He hurt us there," Cook said. "There've been times when we've played really well against him. We're going to have to draw on that. We can't brush the issue, he's hurt us in this game and we're going to come back and show our ability in the next game."