While Arsenal, Leicester and Chelsea all came unstuck on their travels at Sheffield Wednesday, Hull and Stoke respectively, Martinez's Toffees sealed their quarter-final spot with a 4-3 penalty shoot-out success over Norwich at Goodison Park
That ensured Everton would be in the last eight of the League Cup for just the second time in 28 years as they bid to end a trophy drought that has lasted since the 1995 FA Cup success.
However, Martinez, who is no stranger to cup shocks, having guided previous club Wigan to FA Cup glory, was keen to downplay the impact of other clubs' exits on his own team's aspirations.
"Unfortunately, no, it doesn't work like that," he said.
"We're delighted we are where we are
In our history it's only the second time in 28 years so we cannot take this lightly
We will look forward to the draw and who we will face, but there's still a long, long way to get into a position to think that you can win a trophy."
The Toffees' progress to the last eight has been far from serene as, for the third time in as many ties, they fell behind.
Canaries defender Sebastien Bassong's opener was cancelled out by stand-in skipper Leon Osman, though, and goalkeeper Joel Robles saved Wes Hoolahan's penalty before Nathan Redmond blazed over to send the hosts through.
After come-from-behind victories over Barnsley and Reading on the road in the previous two rounds, Martinez insists this cup run is building character among his ranks.
"All the ingredients you need to have to be a winning team have been tested in this competition," he said.
"From resiliency, strength of character, never giving up, finding that chemistry between the players, pushing yourself to the limit and then being able to control the big moments
There's been more than just good technical football.
"It's been a competition so far that has built a very strong platform within the dressing room and it's developed very good relationships."
Norwich boss Alex Neil made seven changes to his starting XI and was impressed by the likes of full debutant Youssouf Mulumbu and the recalled Lewis Grabban, who almost won the tie in the 90th minute with a header that Robles somehow clawed away.
Having seen his side concede six in their previous away game at Newcastle, Neil focused on the positives in Merseyside ahead of a daunting trip to Barclays Premier League leaders Manchester City this weekend.
"We can take confidence," the Scot said.
"But that sort of challenge is going to be totally different to the one we've faced
They play totally different in terms of their system and how they try to play.
"We're going to have to try and adapt, do as best we can, try and cause them as many problems as we can and keep it tight at the back."
Source : PA
Source: PA