The veteran midfielder praised the country's supporters after Andriy Shevchenko fired the co-hosts to a 2-1 victory over Sweden in their opening match of Euro 2012 on Monday
Two headers from Andriy Shevchenko cancelled out Zlatan Ibrahimovic's early second half goal and sent the co-hosts to the top of Group D after England and France drew 1-1 earlier in the evening.
After their comeback, the Bayern Munich player praised the home fans, who were in full voice all match, but insisted they must not get ahead of themselves too much with a tough game against Les Bleus looming.
"I want to thank our fans," Tymoshchuk told German television channel ZDF. "It was a surprising athmosphere.
"We were 1-0 behind and then turned the match around into our hands. You could see that we were nervous. Now we have to come down and see what will happen in the next game.
"Like England, France are a strong team. But we have to play with exactly the same aggression and organization in that game."
Ukraine beat Sweden at the Olympic Stadium in Kiev and the 33-year-old joked about the possibility of returning to country's capital for the final on July 1, adding: "Why not?"
Striker Andrey Voronin also commented on their upcoming fixture against Laurent Blanc's side, but withdrew from discussing their match against England, stating that the team will have to overcome Les Bleus first.
Voronin told reporters: "We know about France, and they have a lot of good players like [Franck] Ribery, [Karim] Benzema and [Samir] Nasri. It will be a really difficult game for us.
"We didn’t see them [England] today, first we play against France and we think about France. Then we will look at the next game."
Ukraine face France on June 15 at the Donbass Arena in Donetsk.