There's been a lot of research done on this subject, and the conclusion is that trying to lose weight just by working out doesn't, uh, work out. There are three main reasons why this is the case:
Eating is easier than working out. Eating X calories is a lot quicker and easier than exercising away X calories. There's a lot of inherent trickiness of knowing how much you burn (pro tip: whatever your fitness tracker says, it's probably way more than you actually burn), but if we say it's somewhere between 50-100 kcal/km, it means you have to run somewhere between 5.5-11 km (≈ 3.4-6.8 miles) to burn off the 550 kcal in a Big Mac. Oh, and if you had soda (210 kcal) and fries (320 kcal) with your burger, you'd basically have to double the workout.
Working out makes you hungrier. Your body will notice the energy expenditure and try to replenish its reserves. If you just eat until you're not hungry (i.e. no calorie restriction), you'll likely eat enough to compensate (or maybe even over-compensate) for whatever you lost during workout. (If you're an elite-level athlete this may not be true, but they are exercising for several hours per day, on average.)
Working out lowers your non-exercise energy expenditure. Contrary to popular belief, exercise does not make you burn more during the rest of the day - you'll burn less. This could be because of conscious actions (taking the elevator instead of the stairs because your legs are really tired after that long run), by unconsciously reducing activity (you get up out of your chair fewer times during the day because your body doesn't tell it wants to move since it already did), and even through fully involuntary mechanisms (i.e., your basal metabolic rate dropping).
If you want to lose weight, or more specifically lose body fat, these should be your priorities, in order of importance:
- Restricting calorie intake, since a calorie deficit is the only way you'll actually lose body mass
- Strength training and a high protein intake, since they both improve the ratio of fat to muscle lost (not much point in losing weight if it's mostly muscles - relatively speaking, you'd be fatter afterwards!)
- Cardio, but more for the general positive health effects than for the calories it burns (although it may give you a little more wiggle-room with the calories)
Edit to address OP's edit:
What I faced in while I restricted my calorie intake(even by keeping high amount of protein intake) was more muscle pain, lateق recovery and having not enough energy to workout as before, by the end I felt I am loosing muscle even more than fat!
Why do you think you were losing muscle? It's perfectly normal to feel weaker than usual when cutting; I mean, you are basically starving yourself. A cut isn't something you do for its inherent fun, I'm sorry to say.
You have to consider that when you're on a calorie deficit that the maximum training volume you can tolerate decreases, so you might need to lower it a bit (decreasing weights, doing fewer sets and/or reps). Sounds like this might've been the case for you.
However - since you wrote in a comment to a recent post on a similar subject that you had lost 2-3 lbs, you may have lost neither muscle nor fat - 2 lbs can easily be accounted for by hydration, how much and what type of food you have in your guts, how much glycogen you have stored in liver and muscles, and probably more that I forgot.
Personally, I've noticed that my own weight can easily vary about 1% from day to day when I'm in calorie balance. If I recall my bro-science correctly, the recommended rate of weight loss is roughly about 0.5%/week (so 1 lb/week if you're 200 lbs; more than that and you'll start losing more muscle), so even if you're doing things right it'll be hard to tell if you really lost weight any for the first two weeks, or if it's just the usual fluctuation. My advice is to weigh yourself often (every day in the morning, after any toilet visits but before breakfast), plot the results, and look at the trend rather than what the scales happen to say this particular morning.
The only thing that will see you losing weight is a calorie deficit. This is the hard, cold, nonnegotiable truth. You can certainly try to achieve that by lots of cardio and unrestricted eating. If you're like most people, it won't work because your body will trick you into compensating for the calorie loss, through a combination of eating more, doing less non-exercise activity, and lowering your metabolism. If it does work for you, well, congratulations, you achieved a calorie deficit without a conscious calorie restriction.
As for losing fat, I guess that if you are in calorie balance and you do proper strength training, your body should slowly recomposition to less fat and more muscle. Might take a while though (and it will likely be slower the less flabby you get), so don't count on sixpack abs this summer if you start now.