The Three Lions needed Frank Lampard to convert a late penalty to snatch a point at Wembley on Tuesday, with the Chelsea star's midfield partner Steven Gerrard sent off for two bookable offences.
Hodgson conceded that the current team looked short of experience in attack but is confident that he can get the best out of the Manchester United forward.
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"I've spoken to him of course. He's had a nasty injury and we're hoping he gets over it as soon as possible.
"The sooner he comes back into our fold the better because we are short of experienced and quality front players in England. We are blessed with quite a few very good midfielders.''
A number of young players featured against Oleg Blokhin's team, with Alex Oxlade-Chamberlain and Tom Cleverley both starting the match.
Hodgson acknowledged that the duo had found it tougher than was the case in the previous match against Moldova, but praised the impact of substitutes Daniel Sturridge, Danny Welbeck and Ryan Bertrand.
"This will be a very, very good experience for those five young players who were thrust into the fray and had to battle to get a result from the game," he continued. "Bertrand, Sturridge and Welbeck made a difference.
"It's nice when a player comes on the scene like Cleverley and Oxlade-Chamberlain and they have excellent games [against Moldova] and everyone writes them up and says 'fantastic, we've got two excellent young players here'.
"I'm afraid the flip side of the coin for them is when they play the next game and it doesn't go quite so well the praise will be replaced by a little bit of criticism and it will be suggested they need more time.''
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Cleverley was guilty of missing two good chances to score for England in the midweek fixture and Hodgson noted that his young players could do worse than follow the example of the likes of Lampard when working on their finishing.
"If you're a forward or midfielder it's in your interests to practise your shooting," he said. "Lampard and Gerrard have got a lot of goals from midfield positions and we see [Jermain] Defoe doesn't need many chances to score. Hopefully the younger players will learn from the senior players.''
Hodgson maintained that England were unfortunate to be punished in devastating fashion by Ukraine goalscorer Yevhen Konoplyanka, who beat Joe Hart from some distance to give the away team the lead, but backed his side to make amends in the reverse fixture.
"You are talking about individual technical errors and that's part of football,'' he claimed. "We were just unfortunate that having given it away the guy scores such a wonder goal from 20-odd yards.
"His shot might fly over the crossbar and you forget all about it, but when it goes into the roof of the net you analyse every single detail of how you lost the ball.
"We are more than capable of going anywhere in the world and getting results as we've shown in the past."