There are several common different types of quick release couplings in the power washer world and while it is possible you have the wrong lance and hose supplied with your washer, it is unlikely.

Many quick release couplings don't just connect by pushing but have a sleeve that must be pushed forward, pulled back or twisted or a button to be pressed. Mostly diy level washers have the lance, hose and connector as an assembly and the connector can't be replaced.

Most towns contain many businesses that use heavy duty pressure washers, vacuum cleaners, parts washers and suchlike and inevitably other businesses spring up to cater for the needs of local business providing a wide range of repairs, spare parts and accessories and they of necessity gather a wide knowledge of domestic equipment.
If you have trouble or doubts I suggest you locate such a business near you...