Carlisle boss Greg Abbott says the dismissals of Peter Murphy and James Berrett led to Tuesday's Johnstone's Paint Trophy defeat by Accrington.
The holders led 2-1 on the night despite Murphy's sending off, but eventually lost 3-2 after Berrett also saw red later on in the second half.
"We played really well with 10 men," Abbott told BBC Radio Cumbria.
"However the nine men is a problem because you haven't got a get out and you're overloaded on either side."
Both players will miss Saturday's visit of Hartlepool in League One through suspension.
United's Trophy exit extended their streak of failing to score in the first half of a game this season, while in addition the club have conceded a first-half opener in five of their nine fixtures this season.
"We're really disappointed with the first half showing," Abbott continued.
"We've got to come out of the blocks quicker, never mind scoring in the first half, we've got to be fiercer and more competitive.
"If you are like that then the chances are that you will score, but we missed easy chances first half and that was important."
Carlisle have been Johnstone's Paint Trophy finalists for the last two seasons, beating Brentford 1-0 last term after losing 4-1 to Southampton in 2009-10.