At a scorching hot Athlone Stadium, the Chilli Boys seemed all set for their first win of the season but former Santos striker Erwin Isaacs made them wait a little longer after a clinical 89th minute goal.
"We're happy to take something out of this game," Arendse said.
The former Bafana Bafana number one admitted the Clever Boys were perhaps a little fortunate on the day.
"Well done to Chippa United, it was a very spirited performance," Arendse said.
"It was a sigh of relief for us, to come back from behind, and it's a point we will gladly take away for our trip home."
Arendse wanted the Students to be more clinical in future, and also to maintain their intensity levels for longer periods.
"I think we only played for 45 minutes, to be honest," he said.
"We need to go away and work on it – a game is 90 minutes – but I think we'll improve. As the game went on we improved.
"Chippa were very dangerous. Every time they got a breakaway and a counter-attack they made life difficult for us and they put lots of pressure on us, so we tried to minimise that, but it was difficult to do that.
"It would be easy to blame the weather, but it was like that for both teams, to be honest, so we have got to rise above that.
"Perhaps it was just the finishing touch that let us down."
Chippa coach Roger Sikhakhane, back for his first game in charge after being re-appointed, was clearly agitated after his side gave away some much needed points.
"I'm not happy at all with the result," Sikhakhane said.
"We kept trying to get more goals, but we didn't manage to get the second one, the security goal we needed, and instead we allowed Wits to get the equaliser."
Elsewhere on Sunday, Bloemfontein Celtic staged a dramatic comeback to beat Ajax Cape Town 2-1 at Free State Stadium.
On Saturday, Kaizer Chiefs put on a near perfect performance for 34 minutes against Black Leopards before the heavens opened and extinguished any hopes the Amakhosi had of turning in a convincing result.
Play was abandoned 11 minutes before half-time, with Chiefs leading 2-0, and the match was rescheduled for Wednesday night at the same venue. The teams will start from scratch.
Meanwhile, Roger de Sa was successful in his first match in charge of title holders Orlando Pirates, although the Buccaneers struggled to overcome 10-man Platinum Stars, eventually settling for a hard-earned 1-0 victory in Phokeng.
SuperSport United romped to a 3-0 drubbing of AmaZulu in Polokwane, while Golden Arrows defeated Mamelodi Sundowns 1-0 in Durban to put further pressure on Johan Neeskens, the Brazilians' head coach, after their third loss in four games.
On Friday, Maritzburg United and Free State Stars earned a point each, after playing to a 1-1 draw in Pietermaritzburg, to share top spot in the table.
A brace by Mame Niang helped University of Pretoria to a 3-2 win over Moroka Swallows in Dobsonville as the Premiership newcomers remained unbeaten in the top-flight campaign, settling in third position after four games. – Sapa