I've had similar on a tight connection, I made it to the gate with plenty of time to spare - boarding had only just commenced.

Staff just shrugged and said "oh, the system thought you wouldn't make it, sorry", and gave me a new boarding pass for the later flight. I reluctantly accepted it, agreeing it was a close call.

However if you had time to go to the lounge, sounds like yours wasn't a close call at all, so I'd be even more annoyed in that situation.