Ricciardo's progress was halted by the hand injury that he received at this third appearance in Zandvoort, which cost him five races.
However, in Mexico he stunned the F1 paddock by qualifying fourth and hanging on to a valuable seventh place in the race.
Tost, who steps back into an advisory role at the end of the season, says he knew that Ricciardo – who drove for the team in its Toro Rosso guise in 2012 and 2013 – would get up to speed.
"Absolutely no doubts," he told Motorsport.com. "I didn't have any doubts, because he's experienced, and he couldn't have lost the ability to drive an F1 car fast.
"Once you know this, you don't lose it. And what he missed maybe in the past was the trust in the car, trust in the team. Therefore, he couldn't perform on the level which we know he is normally able to do."
Tost conceded that even though Ricciardo looked quick from the start of the Mexico City GP weekend the Australian had exceeded expectations in qualifying.
"It was a positive surprise," he said. "I expected him to be within the first six. But to be in the fourth position was really good.
"A very good performance in qualifying as well as in the race, especially at the beginning, when he could keep Lewis Hamilton behind him.
"And for Daniel, I think the red flag was not good. Because this cost him some of his performance because we had to use the same hard tyre after the restart once more. And this was a disadvantage.
"But nevertheless, he drove a very, very good race and he brought it home in the seventh place."
Tost stressed that the resurgent Ricciardo will play a significant role in the team heading into 2024.
"It's very important because the team needs one experienced driver," he said. "And Daniel is the absolute right choice. And I said to him, it's good now, because now you're in the race mode. And we are looking forward now to Sao Paulo."
In the last two races, AlphaTauri has scored 11 points and moved from 10th to eighth in the constructors' championship.
Williams is 12 points ahead, but Tost says that his team can target seventh place over the remaining races.
"I expected sooner or later that the team would make points because we were not as bad as it looked like," he said of the late surge. "But we were a bit unlucky in the past, especially with Daniel in Zandvoort.
"And I must also say that engineers especially on the aero side made some big steps forward, the updates which they brought to the car worked. And it's quite important that we achieve now on the aerodynamic quite a good performance.
"The seventh place could be possible because we are 12 points behind if I have it correct. We just made 11 points now in two races. We have another three races to go.
"If we get everything together, maybe we will come close there, maybe we can beat them. Of course that's the target."
