For your pump to be most efficient it needs to pump water only once primed, not a mixture of water and air.
Hozelock fittings are usually fine on the delivery side of the pump.
However, the problem with hozelock fittings on the supply side of the pump is that they are designed to have water pumped through them, not drawn (sucked) through them. When drawing water through them it is highly likely that you will draw air past the ‘o’ rings as well as they are designed to stop water escaping under pressure not air ingress under negative pressure.
For this reason the supply side of your pump needs to be completely airtight. This can best be achieved with the hose clamped to the correct Sureflo adapter as another poster has mentioned.