Newbie bike question

Hi There --
Earlier this summer I decided I wanted to try doing a triathlon for the first time. I trained on my own and completed the race yesterday! 650m/20km/4km sprint in 1:43. Not dead last, but ok given my troubles with the swim.

However, my question here is in regards to my bike. I purchased a "hybrid" bike earlier this summer as I wanted to do this triathlon, but also have a 'general purpose' bike for riding around town (to work etc). This was not a cheap bike ($1500), but yesterday it was clear this bike isn't much better than a MTB in the triathlon (I've been lectured by the bike shop that this isn't a mountain bike & I had been riding it too rough (off a few curbs).

Is it worth updating this bike with some new components to make it more tri-friendly? What would you add if you had $300 or so to spend? I don't really want to get a new bike at this time.

Do I just need to keep riding this bike & get my fitness up? The 20km ride took me 51minutes.

Brand: Norco.