The game is England's first competitive match since their tame World Cup exit.
Hodgson said: "We have to play well and do well here. If the result costs us we have to make sure we learn from losing the battle and win the war.
"Winning this game does not make a great team in 2016. Neither does losing it make us a poor team in 2016."
Monday's game marks the start of England's qualifying for the tournament in France, which will see 24 teams compete at a European Championships for the first time.
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After playing Switzerland, Hodgson's side will play a further nine Group E games over the course of the next 13 months as they look to secure their place at the finals.
The top two in each group will qualify for the tournament automatically, along with the best third-placed side. The eight other third-place sides will then contest play-offs.
England's last competitive game was the goalless draw in a dead rubber against Costa Rica in Brazil in June, which saw them go out at the group stage after defeats to Italy and Uruguay.
Hodgson, who was appointed England manager in 2012 and led them to the quarter-finals of the European Championships that year, admits the pain of the World Cup still lingers.
However, he claims arguably the most testing fixture in England's Euro 2016 group does not mean a completely fresh start as he looks to build towards the European Championship finals in two years' time.
"We are not in an embryonic stage," he added.
"We are carrying on, despite the massive blow of the World Cup. It's not a totally new team.
"Alex Oxlade-Chamberlain, Ross Barkley and Raheem Sterling were working with us before and so they're not new, but it's an early stage. We have to make sure after these next two years that we are very, very strong."
The game against the Swiss follows on from England's unconvincing 1-0 friendly win against Norway at Wembley last Wednesday, after which Hodgson was visibly angered when confronted with the statistic that his side only had two shots on target, including Wayne Rooney's winner from the penalty spot in the second half.
Asked whether he was now seeing the nasty side of being England manager after post-World Cup criticism, Hodgson said: "There is no nasty side. I love this job. It's a magnificent job. To have the chance to coach your country is the pinnacle of any coaching career.
"Am I aware that after the World Cup and the enormous disappointment that followed there may have been a slight swing in popularity? I'd have been surprised had there not been.
"I will have to live with external ideas and thoughts and accept them. I'm sure we will never really be able to explain to people how badly we felt on the plane home.
"It's all very well being asked how you feel - you put words to it - but the feelings we had in the dressing room after the Uruguay game in Sao Paolo will live with us for a long time.
"It is now up to us to perform well and play well. Is it enough to come here and play 10 behind the ball and sneak a 0-0? No, I'd say it isn't."
In contrast to their visitors, Switzerland are surrounded by optimism following a credible World Cup which saw them lose unluckily to Argentina in the last-16 after a late goal from Manchester United's £59.7m British record signing Angel Di Maria.
With the lesser lights of San Marino, Estonia, Lithuania and Slovenia making up the rest of Group E, Monday's game at the St Jakob-Park could go some way towards deciding who tops the section.
Manager Roy Hodgson insists England's immediate future will not be shaped by their opening Euro 2016 qualifier against Switzerland in Basel on Monday.