If electrical connectors in a computer don't fit, that's by design. They are keyed so that you can't plug them in incorrectly, so don't force them.
If you read the motherboard manual, it may indicate whether the CPU can be run with a single 4-pin power feed, or if it requires the 8-pin be fully populated to work correctly. On some motherboards, under certain loading conditions, this is optional, but read your manual to know.
The easier option however is to take the previous two posters' advice and just replace the power supply. A power supply at this point in time that only provides a 4-pin CPU power feed is likely to be of poor design quality, or very old.
Another option is an adapter, but most folks don't recommend them as, connectors are usually omitted from power supplies because the power supply is cheap, and the manufacturer doesn't want you to exceed it's limits.
Adapter link