Wales may only have picked up their first points of their Euro 2012 Group G campaign with a 2-1 victory over Montenegro last month, but the manner of that win and the encouraging display in a 1-0 defeat to England mean that football fans in the Principality can look forward to the fixture with optimism.
Despite currently sitting bottom of the section, Wales can still potentially finish as high as third, and Speed believes if his players can learn to deal with heightened confidence among supporters it will stand them in good stead as thoughts start to turn to the 2014 World Cup qualifiers.
"The way the group started was disappointing," he said.
"But with me coming in as a new manager we had to put certain things in place before we talked about results.
"We had a good result against Montenegro and a good performance against England, but we will need to improve a lot more and in every game we need to make a progression if we are to get where we want to be.
"It's good there is expectation and if we are going to be successful, expectation is something we will have to deal with.
"The England performance was okay but the most encouraging thing was I looked at the video again and saw that we can play so much better, there is so much more to come and hopefully that expectation can bring that out of the players.
"The most important thing is to keep improving and if we finish third it will give everyone confidence and show we are moving in the right direction."
But Switzerland will prove a tough test at the Liberty Stadium, particularly as they still harbour hopes of securing qualification for next summer's finals in Poland and Ukraine.
They currently lie just three points behind Montenegro, who they face in their final game on Tuesday, in the race for a play-off spot.
And Speed, who highlighted 19-year-old Basle winger Xherdan Shaqiri as a danger man, said: "They need to win, they are in a good run of form and are playing well.
"They have dynamic forward players that can cause any side problems, but so do we and we need to make sure we cause them problems."
Speed also insisted that James Collins still has an international future despite the Aston Villa defender's withdrawal from the squad earlier this week.
The 28-year-old missed the Montenegro win due to suspension, and it cost him his place as impressive Cardiff youngster Darcy Blake was selected for the following game against England at Wembley.
Collins was named in Speed's panel for this final qualifying double-header, but he withdrew due to a foot problem, although he played 90 minutes for Villa on Saturday.
That had led to speculation that Collins was considering his international future, but Speed said: "I spoke to James, he had an injection in his foot before the game on Saturday, maybe he should not have played but James being James he did. He is struggling and has to let that settle down.
"Darcy has done really well and James was disappointed he did not start against England and I am glad he was disappointed. I would have been disappointed, there was no one more disappointed than me when I didn't play, but James understands that and he is fine.
"James is a big part of our future and is playing well for a club at the top level. So we need him and, as I say, he is a big part of our future."
Blake is again set to partner Ashley Williams in the heart of the Dragons defence with QPR's Danny Gabbidon also on a lengthy injury list that includes Robert Earnshaw, Danny Collins, Joe Ledley, Andy King and Jack Collison.
David Vaughan and Craig Bellamy are available again after missing out against England through suspension, although the Sunderland midfielder is struggling with a bout of tonsilitis.
Ledley's absence means that Swansea midfielder Joe Allen is set for his first international start, with Wolves' Dave Edwards likely to take a bench spot after recently returning from a lengthy injury absence.