The Spaniard made a host of changes from the team that were thrashed at home by Manchester United but the new-look side slumped to a 4-1 defeat at Bloomfield Road.
Blackpool's win extends the Latics' run of consecutive defeats to three matches as Martinez continues his stuttering start at the DW Stadium.
The 36-year-old was particularly frustrated with the way many of the fringe players, who were given a chance to impress their new manager on Wednesday, did not rise to the challenge.
"There are certain standards that are not acceptable in our club, and the players should know that," Martinez said after the match.
Chance"As a professional footballer you need to be ready for the chance when it comes along. We can learn a lot from this defeat.
"Those who have not been involved in the league games were given an opportunity tonight, but it was not good enough.
"Certain players did not perform, and it is clear this is not what we expected. Overall as a team and as individuals, we handed the game to Blackpool.
"They did not have to work hard for their goals, and it is very disappointing. We were never in contention to win - and now we are out of the League Cup, which I am upset about."
In stark contrast, Blackpool manager Ian Holloway was delighted with the display his side put in as they dominated throughout and killed the game off with a little over 30 minutes gone.
The former Leicester boss thinks that the cold and wet conditions at Bloomfield Road were perfect for the Championship outfit.
But he admitted that an injury to Ishmel Demontagnac, who scored Blackpool's opening goal, put a damper on the night.
He said: "Just about everything went right. We ordered the rain, and it came down just as they went out for their warm-up. I am not sure how many of them actually fancied it - but my lads did.
"The unfortunate thing is Ishmel has done his hamstring after scoring a terrific goal - which will put him back a few weeks."