New-look schedule worries Hodgson
On the face of it, England looked to have been handed a straightforward route to the finals in France.
However with UEFA now spreading games in international breaks from Thursday until Tuesday, Hodgson is worried England will be asked to play the first game of back-to-back fixtures with little preparation time.
England and all the teams involved in qualifying were due to find out their fixtures programme later on Sunday, and Hodgson said: "The thing I'm most concerned about is Thursday."
He told Sky Sports News: "I feel that in our preparations we'll have to deal with top (club) matches on Super Sunday with your channel, which means we wouldn't really get the players to do any real work with them before the Tuesday, and if we were playing on the Thursday it would make our preparations very difficult.
"Thursday-Sunday concerns me because I don't think we'd be able to persuade the Premier League and Sky Sports to bring the best fixtures to the Saturday and it will mean basically we'll get no preparation."
The prospect of a dispute over fixtures is one Hodgson and the Football Association will no doubt be keen to avoid.
Overall, though, Hodgson, who led Switzerland to the 1994 World Cup and steered them to Euro 96 qualification but led before the finals to join Inter Milan, saw England's draw as positive.
"I'm very satisfied," he said.
"I must say the name of Switzerland always brings a smile to my face. They were four fantastic years.
"It's a team we know reasonably well so I was happy with that one."
England have never played Lithuania before, but San Marino have been regular opponents - in 1993 they famously scored after just 8.3 seconds against England after a bungled back-pass by Stuart Pearce.
England went on to win 7-1 - and have scored at least five goals in the four games they have played. Estonia should also pose little problem, with England playing them twice in 2007 and winning 3-0 home and away. Switzerland will be England's biggest challenge, having secured a 2-2 draw at Wembley in qualifying for Euro 2012.
Scotland and the Republic of Ireland will face each other in a Group D battle between two teams led by former Celtic managers, Gordon Strachan and Martin O'Neill.
They join Germany, Poland and Georgia, as well as UEFA's newest member Gibraltar, who were drawn to Group C with Spain but were switched to D for political reasons.
Republic boss O'Neill said: "They will be great occasions I hope. I'm sure he (Strachan) is looking forward to it. I'm sure he'll be as excited as I am myself. It's tough, I'm there's other groups we might have preferred to be in but we'll get on with it.
"Germany you would say are the outstanding side in the group but there's plenty to fight for."
Strachan added: "The commercial manager is happy. Every tie, there's something in it. You've got Gibraltar, new to the competition; Germany, one of the best teams in the world; the Republic of Ireland; Poland, who we play in a friendly - we've just decided to knock that one on the head and the backroom staff are just going to play their backroom staff.
"It is exciting. There's some groups you might call mundane but we're definitely in an exciting group. It's a terrific, terrific draw."
With 23 places at the finals up for grabs - France go straight in as hosts - prospects of smaller nations going through have raisied the stakes. Two teams will go directly to the finals from each group, and the best third-placed side will join them, with four others advancing from play-offs between the eight other third-placed finishers.
Wales boss Chris Coleman said: "Definitely there's a bit of excitement in there; anticipation. Everybody's wondering what's going to happen.
"Teams like ourselves - Wales, Scotland and Ireland and Northern Ireland - it gives us a little more chance of maybe qualifying and reaching a major tournament. The format that's been before is very difficult for us but with the extra teams, who knows? It's all up for grabs."
Manager Michael O'Neill said: "Greece will be a very tough game but it would probably be the country you may have chosen. We have teams in there, the likes of Hungary, Romania and Finland, that I believe we can compete with and take points from.
"We're happy with the draw. We need to maximise our points at home. We're well capable of doing that."