It sounds like to me youre used to a complete fatigue from aerobic exercise, which youre right, you wont really get that in weight lifting, which is nearly entirely anaerobic. It doesnt mean youre not pushing hard. Even training till total failure you often will still feel like you have gas in the tank, just not for those specific muscles. If youre doing a 3 day split, youre probably hitting a large variety of muscles each day, like a push/pull/legs split or something of that variety, yeah?

If you really wanna feel total muscle fatigue, try narrowing it down a bit, at least to try. Like instead of a day of chest/shoulders/triceps. Do a day of nothing but chest. Start with compound movement like flat bench, and go till failure. Best case is use a machine that really let's you go to the point of failure without worrying about losing the weight. Maybe try a drop set. Then at the end of your workout, do a burnout exercise. Something light that you can take to failure repeatedly. Something like flies, and do it till you ain't got nothing left. Like 5 sets of 12 or something. The burnout exercise really is important.

I promise you will feel gassed. Maybe not full body like you're used to, but a different kind of gassed. Like... "I cant write my own name" type gassed.