I bought a Mazda 3 2012 new and the first few miles off the lot and for a short time on the freeway, I was driving in manual mode (mazda 3 automatic transmissions have a manual mode also) without realizing it and only noticed it when I started to accelerate. Anyway, since I was on the freeway, I couldn't slow down and was driving in a low gear for a couple of minutes and since then, it doesn't feel like the car accelerates as it should (kind of sluggish). Is there a chance I damaged either the engine or the transmission? How would you go about diagnosing if there is a problem?
Do you have any indicator lights on your dashboard? As long as you were not bouncing off of rev limiting (your car would of been surging as it bounced off of rev limiter) the car should be ok. The car should be under warranty, so I would take it in and tell them it doesn't seem to be performing right and have them take a look at it. They should do it for free.
Assuming there is an issue, start with the trouble indicators on the dash if there are any. If there are none, you can reset how the cars ECU by pulling the negative battery cable off of the battery, letting the car sit for a bit then connecting it again. It will cause the ECM to relearn the engines parameters. If the check engine light is on, you can take it to you an autoparts store and they can plug in a computer to tell you what is wrong.
If the car is idling noticeable rough and chugging, you may have done something to the engine internally and a compression test should be administer to verify you are losing compression.