"I am partly frustrated, partly disappointed, partly very proud of the players. I thought some of the football we played sometimes was amazing," Baxter told the media after the match.
Wits captain Sibusiso Vilakazi broke the deadlock in the 23rd minute, but Chiefs equalized via Katlego Mphela eight minutes before halftime, both goals came from spot-kicks.
"I think to give that last effort in the final 15 minutes of extra time, after the schedule that they have been through, is probably more than expected," he added.
The home team restored their lead two minutes into the second half, when Wits striker Sthembiso Ngcobo slotted home from close range. The lead only lasted for eight minutes, as Chiefs midfielder George Maluleka equalized for Amakhosi.
"In penalties there's a winner and a loser, a couple kicks of the ball and you dead. We faltered a little bit, but we came back. We tried to win it, we couldn't. Penalties is what it is," he said.
"So congratulations to Wits and good luck to Gavin and his boys in the final. If you have been a Kaizer Chiefs fan this season, you want silverware. But there are a lot of positives," he concluded.
Meanwhile, Bidvest Wits head coach Gavin Hunt insisted that his players fully deserved to win the tightly contested encounter.
"Fantastic performance, the boys deserved it, everyone's worked hard. When we lost the league with all those draws. I said to the players at halftime, we won the game, then we gave the game, we won it again and gave it away again," Hunt told the media.
Wits will now face the winner between Orlando Pirates and Maritzburg United in the 2014 Nedbank Cup final.
"We deserved it, the equalising goal was a real schoolboy, Sunday morning football stuff. Right in the beginning of the game, we should have been 3-0 up in the first half, but overall I thought it was a great effort," he said.
The Clever Boys will be participating in their first ever Nedbank Cup final since 2010. The Braamfontein side defeated AmaZulu 3-0 in the 2010 Nedbank Cup final edition.
"Chiefs are a quality side, but we controlled it, we brought Matthew Booth on and it worked. The last couple of weeks have been breathtaking. I won't be watching the other semi-final match tonight," he concluded.