The Arsenal winger believes it would be dangerous to go to Kiev and play for a draw, and was impressed by a midfield trio of Jack Wilshere, Steven Gerrard and Frank Lampard
Roy Hodgson's side moved top of Group H in qualification for the 2014 World Cup on goal difference, after a convincing 4-0 win over Moldova.
A point would keep the threat of Ukraine breaking into the top two at bay with two games remaining in the group, but Walcott says the Three Lions will not sit back despite facing a tough test away from home.
"We always go in to games trying to win them," Walcott told reporters. "We don't want to go out there and try to get a draw. That's when we could be caught on the break.
"We have a lot of pace in this team. They will have to come at us and I think that could work in our favour."
Walcott was also impressed with England's midfield trio of Arsenal team-mate Jack Wilshere and veterans Frank Lampard and Steven Gerrard.
"I bet Frank and Stevie [Gerrard] feel very old next to Jack," Walcott joked.
"It definitely did work, they communicated well and blended well, the rotation worked well and they all had a part to play in the [opening] goal so there are a lot of positives to take from that.
"We have lots of players in that position but they did very well against Moldova."