Blokhin: Ukraine must keep their heads
He also has some work to do to before Ukraine's next test on Friday against former world and European champions France, who drew their opening match against England 1-1.
"We haven't thought about the game against France. I don't know whether I will change the starting line-up or not," Blokhin said of the France clash in Donetsk.
Andriy Shevchenko's two second-half goals on Monday sparked national celebrations that temporarily diverted attention from economic problems and political tension in Ukraine.
The performance was a huge improvement and raised expectations after an unimpressive build-up to the tournament in which Blokhin said his players could not shoot straight or tackle properly.
But he sought to bring them back down to earth by saying he was unhappy with the way they played towards the end of the match, when Sweden squandered several chances to draw level.
"I was disappointed with our performance in the final stages because players did not stick to the agreed game plan," said Blokhin, a former European Footballer of the Year who is never shy of criticising his players.
"We've taken advantage of the draw between France and England but need to play some good football against them to prove we can qualify from the group."
He also complained that Sweden carried on playing when Evhen Selin was down injured and Zlatan Ibrahimovic went on to score the opening goal.
"They didn't kick the ball out as our player was laying on the pitch and scored a goal. This is not fair play," he said.
Shevchenko, now 35, avoided criticising the Swedes but agreed it was vital not to get carried away after the carnival atmosphere in the capital Kiev.
"We mustn't be euphoric. We have two more games to play in the group," he said.
Ukraine looked well-organised for most of the match, giving Sweden little time on the ball, making their physical presence felt and trying to catch their opponents on the counter-attack. They also targeted Sweden's weakness from dead ball situations.
"We knew the Swedes had conceded a lot of goals at set-pieces and worked on it. And it paid off once," midfielder Serhiy Nazarenko said of Shevchenko's second goal, a near-post header from a corner.
Blokhin may still be concerned by occasional lapses of concentration and a defence that allowed Sweden enough chances to feel they deserved a draw.
But he will be heartened by the impact made by senior players such as Shevchenko, Anatoly Tymoshchuk and Andriy Voronin, whose influence grew as the match wore on.
Their steadying influence on the younger players will also be vital as they try to go further than in 2006, when they reached the World Cup quarter-finals.
"We did not expect easy games at the tournament and still have two very difficult games to play," Tym