The hosts lost by 80 runs and Cook accepts that they were second-best with the bat, the ball and in the field.
He said: "We didn't play very well, in all three aspects. We were up with the run rate but never got that partnership.
"We've got three games to bounce back. But against Pakistan we lost the Test series and turned it round in the one-dayers. We've got to look at ourselves and stand up and be counted."
The third ODI - of five - is due to take place at The Oval on Friday.