The Alex boss fielded a youthful side in the 2-1 first-round defeat to the Championship club, with academy product Harry Davis, the teenage son of assistant manager Steve, on the bench.
Thordarson said: "I am happy with the young players coming in, but anyone can see that we need to strengthen this squad. We need a minimum of another three experienced players. However, I haven't been able to attract the players I want to the club.
"The squad is so small, I have had academy players on our bench and they are too young. You can't expect a boy to do a man's job.
"There is a situation about money here, but we need to realise we need to strengthen the team because with two or three players out we are struggling."
Meanwhile, Crewe have made goalkeeper Steve Collis available for a free transfer or loan. Collis has slipped further down the pecking order following the arrival of David Button on loan from Tottenham.