Erasmus is now in credit as South Africa's coach, with seven wins and six losses from 13 matches.
Springbok coach Rassie Erasmus defended the character of Siya Kolisi after the possibility of a citing against his captain emerged in the aftermath of South Africa's hard-fought 26-20 win against Scotland at Murrayfield on Saturday.
Two well-taken penalty goals in the second half, one each by Handré Pollard and Elton Jantjies, eventually clinched the match for the Springboks.
However, Scottish flanker Hamish Watson crossed the chalk and Greig Laidlaw's conversion tied the score at 17-17.
'The current world rankings don't indicate how tough it is to come and play here and we could have lost the game in the dying minutes.
Crucially, in his team's last four matches on the road, they have beaten New Zealand, been unlucky to lose 12-11 to England and claimed back-to-back victories against France in Paris and Scotland in Edinburgh.
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Erasmus, though, mentioned the Boks they will not get carried away this win over a very risky Scotland side.
'We're learning how to close out games and that's why we won this game because Scotland were as good as us on the day, ' Erasmus added.
"The maturity of this team is starting to show because we are now winning games from tight situations".
'We did well at the breakdown, especially our work at the defensive breakdown where we managed to win vital turnovers at important times'. "We scored three points when Willie le Roux was off the field with a yellow card and they didn't score".
Erasmus also lauded 21-year-old Embrose Papier, who made his first start in the No 9 jersey for the Springboks and had a good game next to Pollard.
South Africa coach Rassie Erasmus told reporters post-match he was aware of the alleged headbutt but said "I know the man and it would surprise me [if it was deliberate]". We thought this was the right game for him, on this pitch and the way Scotland play suits him well, and he also handled it very well.
"I really haven't seen it", said Erasmus, whose team finish their European tour against Wales in Cardiff next Saturday.