The majority of Hodgson's 23-strong squad, including new skipper Steven Gerrard, met up at their Manchester base and will have their first training session with Hodgson this evening.
They will stage their first public session tomorrow [Thursday] before flying to Oslo on Friday for the friendly international with Norway the following day.
Former England striker Shearer, who netted 30 times for his country, said: "It hasn't been an ideal preparation. That is clear for everyone to see.
"We didn't have a manager, which in turn meant we hadn't got a captain. Thankfully they (the FA) have made the decision, Roy is there and he can look at everything he has to do.
"On the other hand, no-one is expecting us to go and win it, which is totally different.
"Every tournament we normally go into, the talk is always about the players we have to win the tournament, and that we are going to win it. That might help us.
"But England are in a really tough group. It seems as though France have turned a corner. They will be a lot better than they were in the last tournament, which wouldn't be difficult.
"With Sweden, historically, we rarely have decent results against them and Ukraine in their own back yard will be tough. We will do well to get out of the group and go on from there."
Shearer believes experienced performers like Gerrard and fellow midfielder Frank Lampard still have key roles to play after claiming the crop of young players have not progressed as hoped.
He said: "When we started the season, we were all full of expectation about the number of young players who were coming through and the old guard were being phased out.
"If you look at Manchester United in the Community Shield, there were Smalling, Jones, Welbeck and Cleverley. Smalling and Jones have had okay seasons, Cleverley has been out injured and Welbeck has had good times.
"But they haven't kicked on as much as everyone thought and felt was going to happen with this new generation.
"Lampard and Gerrard, in this tournament, still have a part to play with England. I don't think there is any doubt about that."
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Shearer believes Spain will be favourites to triumph next month.
He said: "Spain will win it. I have tipped them for the last two years. I don't see any reason why that should change.
"Germany might push them all the way and Holland will be there or thereabouts.
"Rather than expecting, I am hoping England win it. I would love to talk about England lifting Euro 2012. That is utopia for me."
Tottenham midfielder Scott Parker will be looking to prove his fitness to Hodgson after being troubled by an Achilles problem during the latter part of the season.
He has until May 29 - the final date for submitting squads to UEFA - to convince Hodgson he has overcome the injury.
Liverpool midfielder Jordan Henderson is on stand-by should Parker be ruled out.
Reds defender Martin Kelly was also due to train with the squad after being drafted in as cover by Hodgson for the Norwegian encounter.
The former West Brom boss has 19 days and friendly internationals against Norway and Belgium to hone his plans and ideas before the Euro 2012 opener with France on June 11.
The Chelsea contingent of John Terry, Ashley Cole, Lampard and Gary Cahill - plus stand-by player Daniel Sturridge - have been given extra time off after the club's Champions League triumph.
They will not report for duty until next Tuesday while Manchester United striker Wayne Rooney is working to the same schedule after playing with a minor injury during the latter part of the campaign.