Goals from Ishmel Demontagnac, Ben Burgess, Charlie Adam and substitute Gary Taylor-Fletcher gave Blackpool a comfortable 4-1 victory at Bloomfield Road.
Martinez, who arrived in the summer from Swansea and has now seen his side lose three successive matches said: "There are certain standards that are not acceptable in our club, and the players should know that."
He added: "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."
Demontagnac is hoping to get his career back on track after being sacked by Walsall last November.
However, he could be sidelined for several weeks after pulling up with a hamstring strain in the second half.
Blackpool manager Ian Holloway was thrilled with his side's performance and 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."