Guardiola confessed after Manchester City's well-fought 2-1 win over West Bromwich Albion that the the tie was 'a waste of energy', while Mourinho suggested that Manchester United would not miss the competition if it was axed.
Wenger, whose side set up a fourth-round tie with Norwich City by edging past Doncaster Rovers, believes that each competition must be taken seriously due to the growing pressure on managers to lift silverware each season.
"You cannot sacrifice deliberately any competition with the pressure that every club is under now," the Frenchman, who has yet to win the cup in his 21 years with the Gunners, told reporters.
"You know that you could pay the price sometimes for it because you know that if you go further in the League Cup, at some stage you play in the semi-final - home and away in January. So you have the FA Cup, the Premier League and sometimes you lose players in these competitions."
Man City will play host to Wolverhampton Wanderers in the last 16 of the EFL Cup, while Man United travel to fellow top-flight side Swansea City.