The 46-year-old, speaking on Tuesday in the unlikely surroundings of Donetsk's Chamber of Commerce building where France hold their media briefings, also said England needed to be more adventurous if they wanted to progress.
Blanc said he still believed Spain remained the favourites to retain their trophy despite their opening draw with Italy.
"We need to show more self-belief and assurance in these type of big matches," he told reporters after France stretched their unbeaten run to 22 matches with Monday's 1-1 draw.
"They [England] dominated us for the first half-an-hour and we could have collapsed. If [James] Milner had taken his chance, we could have been 2-0 down after 30 minutes and that would have made it very difficult for us to come back.
"If you are shy and if you don't take risks you will get punished. We should have played with more width than we did and that is something we have to work on.
"We are going to evaluate all of this and decide if we have to make any changes because the game against Ukraine is going to very tough, very complicated for us."
England took the lead after 30 minutes when Joleon Lescott thundered in a header but France equalised nine minutes later when Samir Nasri scored past Joe Hart. Lescott, Nasri and Hart all know each other well as team mates at Manchester City.
England's defence otherwise stood firm but Blanc said they needed to be expand their horizons if they wanted to make an impression at the tournament.
"They played a kind of false pressing game with their two front men but, in reality, they stayed very deep around 60 or 80 metres from our goal and they gave us space to create," he said.
"But we did not do enough, and they will have to have more attacking ambitions if they want to win games and progress.
"However, they are very difficult to beat in the air, and no-one will find it easy to beat them."
France and England, with a point each, trail Ukraine who top the group after their 2-1 victory over Sweden thanks to two goals by talismanic striker Andriy Shevchenko and Blanc said he was delighted that the old warrior, now 35, had scored.
"I read an article four or five days ago that said he had such bad back problems that he could not even walk, never mind train," said Blanc.
"Well the Ukrainian idol gave the best answer to that article with his two goals to prove that the big players are always ready for the big tournaments and he has given hope to his country.
"This really makes me happy, because I know him personally and I like him."
Blanc added that having watched all 16 teams, he still thought Spain remained favourites to win the tournament after their 1-1 draw with Italy, although he was also impressed by Russia's 4-1 victory over the Czech Republic.
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