The Edinburgh lock wore the captain’s armband for the first time as Scotland snatched a 21-19 win over the Pumas with a penalty from Duncan Weir in the closing stages.
Argentina, who had led by nine points with 11 minutes to play in Cordoba, then spurned a late drop goal attempt.
Gilchrist praised his colleagues for keeping the faith and made sure to single out the forward line for praise.
“It wasn’t perfect but we showed a bit of character in the last 10 minutes and that is something I am really proud of,” he said.
“I was just saying ‘keep believing in what we have been doing all week’.
“I think it was a scrum that was the turning point, we pushed them off their ball and got three points to put us within seven and then great individual play and a great score took us right back in it.
“Then we had to score again and our forwards really stepped up. I am really proud.”
Scotland boss Cotter believes the confidence generated by the come-from-behind triumph should stand his team in good stead for the battles still to come.
Next up for Scotland is a showdown with South Africa in Port Elizabeth on Saturday, June 28.
“There is a big difference between losing by a couple of points and winning by a couple of points,” Cotter said.
“We will get confidence from this because we came back from a difficult situation. We perhaps didn’t score when we could have scored but we kept at it, we kept building and constructing our play.
“We will keep our feet on the ground, we know next week is going to be harder.
“There were some every positive things in this display, though, the line out, the scrum, even launching the play off the set phase, we just need to keep the ball a bit more.
“I think we constructed and produced more play this time I am glad that we believed enough to keep the ball and come back from 19-10 and score the necessary points to come away with a win.”
Cotter was particularly encouraged by the final 10 minutes in which his team, staring at defeat, managed to manufacture three scores to snatch the result.
He added: “We started holding the ball a bit more often and set simple objectives of just getting over the advantage line.
“I am really happy to just see players find space and be able to vary our play and score tries.
“It is not perfect, we know exactly that. We found ourselves in a couple of situations five feet from their line and got turned over and did not score so we need to work on our work together.
“It was a positive result. We have some very good players who know how to express themselves.”