Boro followed up their FA Cup scalp of Manchester City in January by eliminating Manchester United on penalties in the same city on Wednesday night in front of 10,000 travelling supporters at Old Trafford.
Their reward is a quarter-final clash with Martinez's Toffees at the Riverside in a contest that will pit Karanka against his "good friend" and the man who took him under his wing when he first arrived in England in 2013.
"If I have been successful here since I arrived it is because Roberto gave me a lot of advice," Karanka said.
"I have to say my gratitude again
He's a good friend who is doing really well and I'm really pleased to play against them.
"I know him when I came here because he sent me a letter to say welcome
He called me and we had a really good chat
He was telling me a lot of good things and I learned a lot from that chat
We worked together two weeks ago in Spain in the Spanish Federation."
It was another Spaniard, Middlesbrough's back-up goalkeeper Tomas Mejias, who was the club's hero in the round-of-16 shoot-out as he saved from England captain Wayne Rooney and Ashley Young in Boro's 3-1 success
The 26-year-old began last season as the first-choice stopper but lost his spot to Dimi Konstantopoulos and has been restricted to four appearances this term, all of which have come in the Capital One Cup, so Karanka was delighted to see the former Real Madrid trainee claim the spotlight.
"He did well in the game and he played well in the previous three games that we played to get here," Karanka said.
"I am really pleased with him because I know him since he was a kid
He was at Real Madrid in the academy and last season he lost his position on the pitch
Everybody could see that he was a really good keeper."
Karanka admitted being surprised by the starting line-up Louis van Gaal deployed at Old Trafford, with James Wilson, Jesse Lingard and Memphis Depay all given a chance to impress.
However, the fact that the Dutchman had turned to substitutes Rooney, Young and Anthony Martial by 71 minutes was an indication of how well Boro played
"They finished the game with all of their players and they have an amazing squad," Karanka noted.
"I am sure that Van Gaal is an amazing manager with a lot of experience and he knew how good we could be.
"They have a lot of games and they have a lot of players with a lot of quality; I don't think he underestimated us."
Source : PA
Source: PA