Hodgson: 'It is still very tight'
Following the Kiev stalemate, home victories against Montenegro and Poland next month will ensure the Three Lions' place at next summer's finals in Brazil.
However, if they slip up at any point in their remaining Group H games, the play-offs or worse beckon.
"It is still very tight," Hodgson said.
"We knew a victory would put us in a good position and a draw would maintain our leadership and make certain going into the last two matches at Wembley we have our fate in our hands.
"I am more than happy we go into these last two games at Wembley top of group and have one more point than rivals. That is positive as far as we are concerned."
Not everyone was similarly enthused.
Gary Lineker, the second-highest goalscorer in England history, was amongst those less than impressed, posting a series of Tweets bemoaning England's inability to retain possession.
"We're seeing a lot of one touch football. England have a touch. Ukraine have a touch. England have a touch...," he wrote.
"When you see England pass it like they've never been introduced to each other, it does make you wonder why Carrick doesn't feature.
"We're on the precipice here. KEEP THE BALL."
In addition, in a Tweet he subsequently deleted, Lineker said: "Awful. What happens to some of these players when they pull on an England shirt?"
Finally, Lineker said, with more than a hint of sarcasm: "Good result for England....Brazil, Spain, Germany, Argentina et al, you're in big trouble!"
When informed of the criticism, Hodgson was not happy.
"I cannot comment on what people think at home. I don't think that is a fair comment on our performance," he said.
"If the expectations upon us are so great we come to places like Ukraine and expected roll teams over, it will be difficult for us to ever get a good result.
"I will stick to my ignorance.
"I think it is a good result. I am surprised that has not been the reaction back at home.
"Who are we talking about? There are 60million people back there. I find it a difficult one to answer.
"Before coming here, the feeling amongst you people was that a draw would have been a good result.
"I am surprised to hear people say what I thought was a good performance has become yet again underwhelming."