The Toffees crashed to a 3-0 defeat at the Liberty Stadium on Tuesday night, as goals from Nathan Dyer, Gylfi Sigurdsson and Marvin Emnes earned 2013 cup winners Swansea a spot in the last 16 of the competition.
Martinez was disappointed with the result but felt there were plenty of positives to be taken after making seven changes from the side which lost 3-2 to Crystal Palace in the Barclays Premier League on Sunday.
"We were looking for individual performances after making so many changes and we got that," Martinez said
"Some individuals performed in a fantastic manner and I know they're going to help the team really well
"To see someone like Bryan Oviedo perform so well after a long injury was very pleasing, to see someone like Tony Hibbert after a long spell out from injury and play 90 minutes was very pleasing, to see someone like Antonin Alcaraz complete the 90 minutes was pleasing.
"To see someone like Luke Garbutt be a real sign of a player we are trying to develop at Everton and Darron Gibson play 90 minutes after 10 months out with injury was pleasing, so there were many positives in individual aspects."
Everton head into Saturday's Merseyside derby against Liverpool at Anfield having lost their last two games and conceded six goals in the process.
But Martinez said he is not worried by recent defensive frailties or the form of goalkeeper Tim Howard, who had a particularly shaky afternoon against Palace and was beaten three more times at Swansea.
"I'm not obsessed about it, we kept 15 clean sheets last season and we are a team that can defend and keep clean sheets," Martinez said.
"I'm not concerned, even if you don't want the feeling you get when you lose football games.
"If he (Howard) had been a young goalkeeper maybe you think how he might be affected by those experiences.
"But he is in the best moment of his career and has got the control and experience (to deal with it).
"Those moments happen but we win and score goals as a team and it's the same when we lose and let in goals."
Garry Monk admitted victory against his former Swansea manager was special, Martinez having been in charge at the Liberty Stadium between February 2007 and June 2009 when Monk was the club captain.
Martinez also won their two previous managerial meetings last season, Everton beating Swansea at Goodison Park in both the league and the FA Cup.
"I did owe him one after they beat us twice last season, but I do not see it like that," Swansea boss Monk said.
"It was a good night, three goals and a clean sheet.
"We played well against a strong side and it was a very good performance in a competition this is very important to myself, the team and the fans."
Monk confirmed after the game that Swansea are close to extending winger Wayne Routledge's contract by another year to 2018.
"We are talking to Wayne and his representatives," Monk said
"He has found a home at Swansea and somewhere he can perform at a very good level
"He's been one of the most consistent performers in my time as manager and hopefully we can get that contract sorted as soon as possible."
Source : PA
Source: PA