He added that it was believed that within Nato, "Britain fights; Germany pays, France calculates; Italy avoids".
In a statement Ainsworth refuted Joyce's comments, saying that the war in Afghanistan was key to the UK's security.
"We will not walk away from that responsibility," Ainsworth said.
"The picture he paints is not one that I nor many people within the MoD [Ministry of Defence] recognise, whether military or civilian."
Last month the UK suffered its 200th troop death in Afghanistan since 2001.
Questions have in turn been raised about the suitability of the UK mission and whether it has adequate resources.
There are currently about 9,000 troops in Afghanistan.
The UK entered the country in 2001 in support of the US to remove the Taliban, who were viewed as harbouring al-Qaeda operatives, from power.