In a thrilling game, Glasgow picked up two bonus points but they were undone in the third quarter.
“The big one was the 20 minutes after half time,” said Wilson. “We talk about that period being a very important match-winning quarter and we lost that period three tries to one.
“Two tries went against us, one that bounced nicely for them and one that was charged down so that was a little bit disappointing.”
Glasgow’s scored four tries through George Horne, Johnny Matthews, a penalty try and Jamie Dobie.
Replacement stand-off Ross Thompson saw his kick charged down for Ulster’s fifth try but recovered well to set up Dobie for his score.
Glasgow piled on the pressure in the closing minutes but could not find a way through the home defence.
“Generally we exited poorly but I was proud of our physicality and the effort to get back into the game and we scored some brilliant tries,” added Wilson.
“To come away from the Kingspan with two points is a positive and another was we looked fitter than Ulster in that last 20 minutes.”
Played in front of 10,000 supporters at the Kingspan Stadium – the largest number since the pandemic – Ulster also scored a penalty try as well as touchdowns from Brad Roberts, Marty Moore, Nick Timoney and Nathan Doak.