The 23-year-old put in a blistering performance for Scotland A last weekend when they beat the England second-stringers 13-9 in Newcastle.
A few pundits thought the No.8 might be promoted to the senior side as a result, but Scotland head coach Scott Johnson has kept faith with most of the players who lost to England at Twickenham last Saturday, giving them a second chance against Italy.
"I was disappointed when I found out that I wouldn't be involved this weekend," said Wilson, who will be captaining Glasgow for the first time.
"But I think they are doing the right thing in keeping the core squad together for the first two games.
"They don't want to change too much. It's important to keep that consistency. But I still felt I did pretty well in my game and I reckon I probably made my claim for a cap a little bit stronger.
"I think I have staked my claim, and I'll keep on trying to do it in every match I play. Hopefully some sort of recognition will come.
"Now I've just got to get on with it for Glasgow, not just for the Warriors, but also to improve my chances of getting in the Scotland squad."
Glasgow hold second place in the RaboDirect PRO12 table, and Wilson believes that a run of good results over the next few weeks will bolster their chances of making the end-of-season play-offs.
The fixture list does them a few favours, too, as bottom-placed Zebre, who are based in Parma, have yet to win a PRO12 match this season, and the Warriors' next match is away to Welsh strugglers, the Dragons.
"We have a short turnaround next week because we play the Dragons a week tonight," said the 6ft 4in forward.
"We're looking to win the next four games. This is the most important point of the season for us.
"If we can get wins we can really kick on. But it's so tight in the top six and we cannot afford any slip-ups now."
The Warriors were without a host of big names when they took on Zebre at Scotstoun last September and struggled early in the game.
With so many Glasgow players in the Scotland squad, Wilson knows his side cannot afford to be complacent.
He said: "The players who come in have to be ready for a tough battle. Zebre haven't got a very good record, but they are getting better and they've lost the last few games pretty narrowly.
"It is only a matter of time before they get a win under their belt, so we can't go over there half-hearted. This is a massive game for us and it is not going to be easy."