You are doing nothing wrong.
Without using a flight plan & using gps & nav hold options you will have to make adjustments in your heading for wind.You can even use your rudder and alieron trim tabs that is what they are there for.
After taking off one should try to trim up the aircraft so it will fly hands off without changing altitude or direction.
Like landing with a crosswind you have to crab in order to maintain the propper direction. If you are rusty are not sure how to do this then take some of the lessons it will help alot and explain what you are trying to do. 8)
I watched a learning to fly segment last night on just this subject It is on the wings channel

Here's what we do in the Navy to correct for set and drift

Keep in mind, course and heading are two different things.

The Black line is your intended course.

The Red line is the Actual course

The SET is the DIRECTION of offset. The DRIFT is the SPEED. If you actually calculate the Set and Drift, you will find it is the same as the wind direction and speed. So we don't need to calc that.

The light green line shows our distance of ADVANCE the dark green line going to our location is the TRANSFER.
Double the ADVANCE. This gives CORRECTING HEADING which will provide a COURSE of 090.

Doubling the ADVANCE AND TRANSFER will provide a COMPENSATING HEADING which will provide a HEADING to get you back on track. Once on track, fly the CORRECTING HEADING.

Doing this whole mess of geometry in the air, and on charts, is difficult, but possible.  I'm very versed in Trigonometery so I will follow this with the mathmatical formulas a little later.

ADDED: You know, I got half way through the process when I realized I have 5 formulas.  Screw that. Fly toward the VOR for 3-5 minutes. Remember your offset angle. To correct, (fly the COURSE you want) double the angle. To COMPENSATE, fly triple the angle until back on track. Then fly Double to correct.

Hope I didn't confuse anyone, the geek in me slipped out.