Debutant Clark, 30, finished with match figures of nine for 89 yesterday as he rushed the visitors to a seven-wicket victory inside three days in Cape Town.
The experienced McGrath, who has 542 wickets in 119 Tests, withdrew from the tour because his wife's illness.
''We did make the comment during the game how unplayable Glenn would probably have been on that wicket,'' Gilchrist told a news conference.
''But Stuart has certainly taken up the reins in grand fashion and we are all really thrilled for him.'' Gilchrist did not want to label Clark as a McGrath clone.
''There are some similarities there but I'll refrain from saying he's the new Glenn McGrath,'' he said.
''I don't want to burden him with that but he certainly filled the void beautifully in this game.'' The result came as a blow to the South Africans after their dramatic one-wicket win in the series-deciding one-dayer in Johannesburg last weekend, the home team reaching Australia's world record total of 434 for four with a ball to spare.
South Africa's players will gather again in Durban on Wednesday to prepare for the second Test which starts on Friday.
''The guys are going home to spend some time away from each other and away from the game,'' said coach Mickey Arthur.
''Emotionally and mentally the guys are drained.
''They have hit more than enough balls, they've caught more than enough catches. It's now about getting away and tuning in mentally and getting right for the Test match that's coming.'' Arthur said South Africa needed to analyse the state of their game.
''We need to sit down and think about our Test cricket disciplines again, we need to reassess where we are in Test cricket and tighten up on the basics,'' he said.
''We need to be tighter and more patient in batting and bowling.'' Arthur predicted an improvement in the second Test.
''We'll be ready and adjusted for Durban,'' he said.