The defeat means Sweden go into their final game of the tournament against group leaders France, without a hope of qualifying for the quarter-finals.
Ibrahimovic feels Sweden produced a much improved display than the loss against Ukraine in their opening match, and that their performance on Friday night deserved at least a point.
"I think we were the better team against England. I really do," he told Uefa.com.
"We should be proud of ourselves because we played a good game. We played the opposite way to the first one.
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"We showed more courage and were much better in dead-ball situations. We played just the way we wanted to play.
"In both the games we have played, we were in the lead, but after 60 minutes, we lost it all.
"Why did we lose both games? I don't know. That is something we need to analyse and see what we need to do better, or in a different way."