Regular oil in Chevrolet Trax - was it a mistake?

Is it terribly important

not to put regular oil in my car

When I had my oil changed, I had regular oil put in it. Is that ok or did I make a huge mistake?

You must use oil that meets GMs Dexos 1 specifications to keep your warranty in force. My understanding is that only certain synthetics meet this standard.
If it were my vehicle I would immediately have another oil change done with oil meeting the dexos1 specification and eat the $40-50 charge. The use of oil notmeeting the dexos1 specification may void your warranty. Be sure to keep receipts showing your oil changes and the oil used.
For future reference, with a vehicle that is under warranty I use the dealership for all service work.

That is what we do also . The cost difference means nothing against the possibility of having an adverse effect on the warranty.