The Gloucester scrum-half kicked 21 points and also scored a late try as the Scots defeated Samoa 36-33 in a thrilling contest at St James' Park to secure their place in the last eight for the first time since 2007.
Cotter believes his skipper had an exceptional game and praised his ability to keep a cool head as the pressure mounted in the Pool B clash, before also admitting his own relief at securing a place in the knockout stages.
He said: "Greig had an outstanding game. We were under a lot of pressure; he kept his cool, we kept our cool. We just needed to win, and that's done. We're relieved, but we're proud as well - that was a tough game."
Scotland conceded three first-half tries against Stephen Betham's side and lost Ryan Wilson to a yellow card for a stamp as Samoa put in an impressive display in their final match of the competition.
The pacific islanders still had an outside chance of reaching the last eight themselves if they had won the contest and Cotter praised them for the performance they put in during the match.
He continued: "That was an outstanding performance from Samoa. They've obviously spent this week having a look at how they want to play, and wanted to finish on a high. They threw the ball around, they've got really dangerous players. They were impressive."
Scotland's reward for reaching the knockout stages is a clash with Pool A winners Australia at Twickenham on October 18 after the Wallabies beat Wales 15-6 in their pool decider.