"We conceded a poor goal but still had the strength of character to come back and score two great goals," he said.
"It's the best we've played [during Speed's reign]. It was really, really good. Norway are a good team and caused us problems.
"It was a 4-1 but it just shows the strength we have going forward."
Wales cruised into a 2-0 lead inside the opening 16 minutes as they capitalised on Norway's lacklustre start.
Gareth Bale scored his third in as many matches when his fierce drive squeezed in at the near post, and Craig Bellamy's beautiful curler doubled the advantage five minutes later.
"The first 20 minutes I thought we were sensational," added Speed after seeing Wales claim three successive wins for the first time 2008.
"When we went 2-0 up we went a bit complacent, we took our foot off the pedal a little bit and stopped doing the things that got us to 2-0 up.
"You can't do that against team like Norway and they came right back into the game."
Having looked so composed before the break, Wales showed real signs of nerves after a horrendous error by goalkeeper Wayne Hennessey gifted a goal to Norway's Erik Huseklepp.
But Speed says he was encouraged by his side's response as they hit back with two goals from Sam Vokes in the dying stages.
"Norway came out for the second half and played really well," he said.
"But we kept our discipline, kept it tight and limited them to very few chances.
"We've got great players going forward and if we managed to keep it solid at the back we can punish teams as good as that."
At 24th in the Fifa world rankings, Norway are ranked 21 places above Wales and arrived in Cardiff having won four of their last five games.
They were among the top seeds for the 2014 World Cup draw, while Wales were one of the bottom seeds.
Wales captain Aaron Ramsey said the manner of the performance should not be underestimated.
"Norway have been in good form," said the Arsenal midfielder.
"They've proved to be a very difficult team to many other countries so we're delighted with the result."