Psionic Combat was not removed in Pathfinder so much as it was removed in D&D 3.5. The 3.0 Psionics Handbook (PsiH) was completely overwritten by the 3.5 Expanded Psionics Handbook (XPH), which did not include Psionic Combat.
Psionic Combat was a very bad idea for a large number of reasons, though the main one is simply that it was very out of place: it completely changed how combat worked, and added weird rules that were totally unlike anything else in the system. In fact, 3.0 Psionics was poorly designed on a number of levels. I strongly recommend against it.
The Expanded Psionics Handbook, on the other hand, is one of the very-best designed books for 3.5, and the Pathfinder version, Psionics Unleashed, by Dreamscarred Press is written by a number of people who worked on Expanded Psionics Handbook. I suggest you go with the Psionics Unleashed and never look back to the 3.0 version.
For an excellent (and humorous!) description of what was wrong with Psionic Combat, I turn to this fairly well known post by AntiDjinn on the WotC boards:
I have used this model before, but to really appreciate how this "class feature" worked you should see how it would apply if ported to mainstream D&D where they haven't been conditioned to accept inferior mechanics without question. Lets take the big sacred moo, a Cleric's undead turning ability:
DM: "Before we get started, Cleric, I just want you to know that I am instituting some changes in your turn undead class feature that will make your class more different and give it a unique divine mechanic."
Player: "OK. How does it work now?"
DM: "Well, for starters, when you attempt to turn undead you will now have to burn a spell."
Player: "A spell???? What level?"
DM: "Different levels. It depends on what turning mode you want to use. Sanctified Gesture takes a level 1, Divine Dance of Power takes a level 2, High Holly Homina Homina takes a level 3, and...."
Player: "Wait, I assume I will get a bonus on the roll based on the level of spell slot I sacrifice?"
DM: "Sometimes you will. Other times you will get a penalty based on the turning defense mode the opponent selects. Turning and turning defense modes will interact on a table. The table determines the actual DC of the roll, not the level of the spell slot burned. Choosing a given defense mode may actually mean you pay a spell to get a penalty on the save, but it will still be better than being defenseless."
Player: "The undead will get defense modes?"
DM: "Sure, so will you. Each round you will select a turning attack mode and a defense mode. In fact, you will need to select a defense mode against each undead opponent each and every round and each will cost you spell slots."
Player: "Wwwwwwhat????!!!!!! What if I am facing undead who do not cast spells, I assume they won't get to mount a defense?"
DM: "It doesn't matter if you face undead without casting ability because their turning and turning defense modes are free."
Player: "Wait a minute! This is stupid! One of my 3rd level spell slots could be spent on Searing Light which fries undead; why would I ever spend it on an attack mode that might help me on a turning attempt? And why would I ever take a turning defense mode, much less a separate one vs. each undead opponent? I would simply choose to ignore undead or cast spells against them or go at them with weapons. I would have to have brain damage to choose to turn with these rules!"
DM: "If you fail to mount a defense then each unblocked undead gets a special +8 bonus to hit you for having this wonderful class feature and choosing not to use it. They also get to drain your stats if they hit. This will apply also to anyone who adds a level of Cleric; multiclassing will be very flavorful."
Player: "But I am a spellcaster, I need to be able to cast spells. How can I do my job if my spell slots get sucked away every time we run into undead?"
DM: "Well, how can you do your job if you are dead or reduced to a mindless state? You need to use your spells this way or you may not live long enough to cast them anyway."
Player: Head down, silently weeping into his hands.
DM: "I should mention too that you will be able to make turn undead attempts vs. nonundead; if you succeed they will be stunned for a few rounds. Of course, everyone who does not have this feature will get a huge bonus on the save DC. The best part: If you blow a 5th level spell to use High Holy Hokey Pokey then everyone in a large area could be stunned for a long while and they don't get a bonus vs. this one mode -- that makes the entire system usable and balanced."
Player: "They should all be stunned if they ever see me willingly use these rules. This is preposterous! I need my spells to heal and buff and perform all the functions of a Cleric. How am I going to be of any use to the party if I hemorrhage spell slots every time we run into undead?"
DM: "That is the beauty of it: You get to choose whether to use your spell slots as they were intended or save your own hide by using them to turn. Come on and at least give it a chance. It will be a mechanic unique to your class so it must be a benefit. You don't want to be just another spellcaster do you? This will add so much flavor and.... Hey! Get him off of me!"
Player: "How ya like that fist flavor?"