England needed a late penalty from Frank Lampard to secure a point at Wembley after Yevgen Konoplianka had brilliantly fired the visitors ahead.
Steven 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, and it means Gerrard and full-back 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 the 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."
The other England players booked against Ukraine were James Milner, Jermain Defoe and Joleon Lescott in a match during which England went behind to a brilliant 25-yard opener from Konoplianka and were grateful for an 87th minute penalty from Lampard after defender Yevhen Khacheridi had handled the ball.
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."
Hodgson rued the absence of the injured Wayne Rooney, Ashley Cole and John Terry and started with Tom Cleverley and Alex Oxlade-Chamberlain in midfield, also bringing on youngsters Ryan Bertrand, Daniel Sturridge and Danny Welbeck.
Hodgson said: "We did a miss a lot of players but the ones who came in, particularly the three youngsters at the end, acquitted themselves well and it is good for us in the future.
"We are not totally reliant on the old guard. We do have young players coming through who can step up to the plate.
"Welbeck, Sturridge and Bertrand made an impact."
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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