The midfielder was not attempting to disguise the bitter taste of defeat to Leicester and said the performance at the Walkers Stadium - particularly in the second half - did not do justice to the huge level of support from the 5,000 fans who made the trip.
"From being 2-0 up and fairly comfortable, giving them a goal before half-time gave them a big lift and they came out in the second half and gave it a right go," reasoned the England international. "We thought we had got a replay back at our place and that last minute goal killed us.
"We are just very disappointed, the fans came up and were magnificent - even at 2-2 they were singing and getting behind us. The worst thing is letting them down.
We were winning games, playing well of late and our league position speaks for itself at the moment
We wanted a Cup run because the FA Cup is massive for this club with the tradition. The fans turned out in their thousands hoping to back us towards Wembley but this year it is not to be.
"Everyone knows we have let the club down by not doing well in the FA Cup and we know we haven't done enough. We are under know illusions, we didn't play well in the second half and paid the price."
However, it is third v fourth at Anfield on Saturday, a crucial encounter on our remaining avenue of potential success this season.
"We have got to look to the next game and we have Liverpool now which is huge for us. We are in a nice position in the league and we must keep on winning there to try and forget about this."
Michael Carrick believes the team must shake off FA Cup disappointment and turn minds quickly towards Saturday's key Premiership clash against Liverpool.