A late Frank Lampard penalty spared England's blushes at Wembley, after Hodgson's men went behind to a stunning 25-yard shot from Yevgen Konoplianka five minutes before half time.
Gerrard, who received a second yellow card for a foul on Denys Garmash, became the 14th England player to be dismissed and their second captain to be shown the red card, the other being David Beckham - also for two bookable offences - against Austria in 2005.
All in all England were shown five yellow cards and a red against Ukraine and it means Gerrard and fullback Glen Johnson, who was booked in Moldova last Friday for kicking the ball away, will now be banned for the World Cup qualifier against San Marino at Wembley next month.
Hodgson, however, criticised Turkish referee Cuneyt Cakir for his handling of tonight's game.
"I thought all the yellow cards were harsh. It was not a game were there were a lot of bad fouls. There were not a lot of fouls full stop," said Hodgson.
"There were far too many yellow cards for the fouls that were committed and we certainly got too many.
"Steven Gerrard is certainly very unlucky to be sent off. I don't think the two fouls he was adjudged to have committed were worthy of that sanction."
Ukraine tested England early on, while Jermain Defoe had a thunderous effort ruled out after a shove into the neck of Andriy Yarmolenko.
But with five minutes of the half remaining, Konoplianka stepped inside Gerrard, then struck a lengthy curling effort over Joe Hart into the top corner to give Ukraine the lead.
In a second-half littered with yellow cards - six of them for England including Gerrard's double caution - Leighton Baines needed to make a timely intervention to prevent Zozulya reaching Konoplianka's cross.
Glen Johnson, among those to get booked after the break, went close at the other end but the introductions of Danny Welbeck and Daniel Sturridge were inevitable given how the game was panning out.
And late on Wellbeck saw a shot blocked in the area by Yevgeni Khacheridi, allowing Lampard to step up and slot home from the penalty mark.
It was Lampard's 26th goal for his country to take him to joint 12th on the England goal-scoring list alongside Bryan Robson.
A defiant Hodgson, however, praised England's performance.
He said: "You are always relieved when you are losing 1-0 and you get a late equaliser. I suppose all games you don't win at home people say it's not a great performance but I didn't think we did that badly.
"We kept at our task. We started poorly in the first 10 minutes but once we got into our stride we had quite good control of the game.
"We went one down to a wonder strike and from then on against a good Ukrainian team you are always going to be up against it but I was pleased with the way we kept playing our football, taking the game to them and creating chances.
"In the end we fully deserved our equaliser so I suppose I'll dodge the question whether it was a good performance or whatever and say that I was very pleased with the way the players went about their task."
Meanwhile, Ukraine coach Oleg Blokhin said: "It was a fantastic start for us. It was a tough game but we created certain problems for England that they could not solve.
"The young players in our squad were probably intimidated by winning against England but no football player is without mistakes. I am very happy about the result.
"It is a positive result because we got a point and we will be in for the leadership of the group with Poland and England and Montenegro. But if we don't get any points with Poland and Montenegro this point is in vain."
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