Pull the left side cover first. Make sure everything is in place the way it's supposed to go. There's a spring on the shift shaft that could be out of place. Your manual should show how this is supposed to go. Take care not to pull the shifter out unless something is out of place and you have to, to get it back in place. Once you pull the shifter out any at all, the internal clutch lever on the other end of the shift shaft will fall off and you will have to pull the other side cover off and put it back on.
Before you go to the other side, make sure your shifter springs back into the center position, after pushing up or down on it. It may not want to shift gears yet, but just make sure it, at least, springs back to center position. Now you can move to the opposite side.
The problem could be on the other side. The internal clutch lever on the other side may have already come off or may be out of time. The other end of the shift shaft has splines on it and the internal clutch lever engages the splines, but it has to be in time. There is a punch mark on the internal clutch lever and an index mark on the inside of the crankcase that has to be aligned. The internal clutch lever is the part that engages and disengages your clutches when you shift gears.
My guess is that the spring is out of position behind the left side cover, but when you move the shifter to put it back in place, the internal clutch lever on the other side is probably going to fall off. So, you will probably end up having to take the right side cover off and put the internal clutch lever in time, by aligning the punch mark with the index mark on the case.
This first picture shows the shift shaft with the return spring on the foot shifter end and the spines, that engage the internal clutch lever, on the other end. The return spring on the shift shaft is what causes the shifter to return to the center position, after shifting either up or down.
This picture shows the internal clutch lever that engages the splines on the other end(behind the right side cover) of the shifter. This is the part with the punch mark that has to be lined up with the index mark on the inside of the crankcase.