Look at the large diameter pipe the goes from the front of the car towards the back. The front end connects to a container with an air filter inside, and the back end connects to the throttle body. The pipe & the filter assembly are what is referred to as the "Induction" and this it what feeds air into the engine, if there is a split anywhere along this pipe (especially in the area that looks like an accordion) then this will allow excess air into the engine (a "vacuum leak"), which can cause the symptoms you describe as the air/fuel mix needed for combustion will be too lean. So have a look at this in the first instance, especially if this is the area that was taped up
Not trying to be condescending just trying to put describe the problem as simply as possible!