The tireless midfielder rued his side's missed opportunities at the Olympic Stadium in Kiev and believes Andriy Shevchenko's first goal turned the game in the co-hosts' favour
Zlatan Ibrahimovic put the Swedes ahead early in the second half, but Andriy Shevchenko headed two past Andreas Isaksson in quick succession to clinch victory and top spot in Group D for Oleg Blokhin's men.
The Lyon midfielder rued the chances in front of goal that his side had spurned and admitted that the difference between the two nations was finishing.
"In terms of chances I thought it was a very even match but the difference between us were how clinical they were making the most of their chances," Kallstrom told reporters.
Johan Elmander and Olof Mellberg both had good chances to snatch a point at the death, but neither were able to take advantage of their opportunities.
Kallstrom also commented on the vitality of the Ukranian side after they had scored their first goal, which sparked life into the team and led to a quick second.
"Of course when they scored they got a lot of energy," Kallstrom added. "[It was] very poor of us to concede from a corner again."
Sweden's next game is against England on June 15 at the Olympic Stadium in Kiev.