It seems like you lack some form of transition between one scene and the next. Moving the player from one UI context to another instantaneously can feel quite jarring. Also, not giving the player any chance to breathe between levels can create a problematic pacing. Both could be what you perceive as a certain "cheapness".
A loading screen is one form of transition, but artificially adding a pointless loading bar which actually does nothing would be quite ridiculous. There are many other forms of transition graphic effects you can use to mentally remove the player from one context and put them into another. Just some examples:
- Fade to black, like DisturbedNeo suggests
- Do some form of wipe transition. This can also be combined with fade-to-black to do a wipe-transition to black and then another wipe-transition from black to the next level. The combination with black might be easier to do because it doesn't require both scenes to be loaded at the same time.
- Zooming in and out again
- Blurring and unblurring
- When entering/leaving a menu, animate that menu to visually move into/of the screen
- When switching between levels:
- pause the game to have the player-character perform an animation
- show a level statistics screen and have the player click/tap a "next" button