Does height of bicycle affect the energy we put to ride?
Short answer: Height does matter (in fact, there are multiple "heights" which you can find out about in the long answer's links), but there are a ton of other factors (e.g. top tube length which is probably more important). The bike's geometry is what determines how well it works for you.

Long answer: What you need is a bike fit (which can be done at most bike shops). Proper bike fitting makes your power delivery good and avoids potential injuries / pain. The handlebars, brake hoods, stem length, saddle height, saddle width, possibly cranks (though unlikely unless you're on the extreme side of heights),etc.  will be adjusted based on your proportions (primarily your inseam as well as your reach) provided the bike can be fit to you. This is highly dependent as well on your riding style (racers don't ride the same way people going on cross country tours do, typically) and feel. Height and inseam are not sufficient (hence why they publish a ton of measurements per bike). I personally prefer a larger size than most people with my height (though I have longer arms + inseam than most people of my height)... See the links below for more details. The most common mistake people make is putting the seat too low (which correspondingly screws up everything else), but you really should start with a bike fit (or if this isn't possible due to financial constraints or something, surveying videos on youtube or something (but I will not link any, since this should be done with a LBS, and test rides)). As the KOPS link below shows, these systems aren't used as an exact science, so the experience of the fitter helps a lot in getting a good fit (the numbers plugged into formulas aren't everything), and it may take a few tries to get something that really works for you. 

A good look on the problems with fit and why its left to the pros at your LBS is http://sheldonbrown.com/frame-sizing.html

As for what you read, it may have been KOPS: http://sheldonbrown.com/kops.html 

There are multiple theories as to how you should setup your bike for "best" cycling. Once you get a fit, you'll end up tweaking it to better suit yourself and changing riding styles. 

Getting tired also depends on how fit you are, and how efficient you are in using your gears - if you start in top gear on a racing bike, chances are you're going to get tired really quickly if you're not pretty fit. It sounds like you have a single speed, which means you have to compromise on one gear for the whole range of riding you do (unless you fit something like a Surly Dingle), so you may need to pick a different gearing combo, though typically these are set with a decent gearing which isn't too hard to start and easy to cruise in (like a 42t/17t on the Surly Crosscheck SS). If you have a fixie, your legs are always moving, so in this case, you may want a flip flop hub which allows you to flip the wheel and let you freewheel a bit when you're tired. Having multiple speeds may help with tired-ness depending on the terrain (hills make you want multiple speeds). 

Getting a bike fit reduces the bike setup part of riding and makes your physical fitness the next problem (and possibly gearing). You may find that the particular bike you have cannot be tweaked to work with your riding needs! (For example, a lot of racing bikes don't work as tourers/commuters).