Ukraine controlled the match in Kiev, with left winger Yevhen Konoplyanka a consistent threat, but for all their pressure, they were unable to find a way past England goalkeeper Joe Hart.
Hodgson's side were happy to play for the point after Ukraine made a lightning start, and although they had good chances of their own, through Theo Walcott and Frank Lampard, England could be happy with a fighting point.
The result leaves England on top of Group H with just two World Cup qualifiers to play – home fixtures against Montenegro and Poland – and Hodgson was pleased with the draw.
Hodgson told ITV: "I thought it was probably a fair result. I thought we did very well, especially in the first half.
"I thought we had clear control of the game and we could have won it in the last minute (through Lampard).
"We gained the result without riding our luck in any way. We gained it because we were very good defensively and we might have even got the goal we needed.
"I don't think that we were that adventurous but it was for them to be adventurous. We had to make sure we controlled them. Perhaps we didn't have the quality there (up front) to make them (chances) count."
The match ended a crucial week for the England squad, with an away point and Friday's 4-0 win over Moldova at Wembley making it a happy one for Hodgson.
"There was 70,000 people here, and it was a big test for the players," he said.
"We've lost seven players from the original squad. We have got to be more than satisfied with the result against Moldova and now the result here."
England – who top Group H with 16 points – sit just ahead of Ukraine and Montenegro, on 15 points each and Poland, who have 13.
And with just two fixtures to play, the stakes will be high in England's next qualifier, a home fixture against Montenegro on October 10.
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