Vieira's charges made a promising start and took the lead just after the half-hour mark through Aston Villa forward Nicolas Jackson. The visitors appeared to be in control as Vieira looked to celebrate his first win since taking charge of the national team.
However, Mozambique refused to surrender and found an equaliser in first-half stoppage time through Geny Catamo, ensuring the two sides went into the break level.
Senegal were unable to find another breakthrough after the interval and had to settle for a point, leaving Vieira disappointed with the outcome despite seeing positives in his team's performance.
"There are obviously regrets. I think we deserved better in the first half. But unfortunately, it proves there are areas for improvement," Vieira told reporters, as quoted by Wiw Sport.
"We have to keep working, because we knew everything wasn't going to be perfect in this match."
The former France international was also encouraged by the contribution of the younger players in his squad, particularly their ability to combine with the more experienced members of the team.
"Young players are selected because they have talent. They have shown with their respective clubs that they have the qualities to aspire to play for the national team," he added.
Vieira believes the team's attitude and cohesion provide a foundation from which they can build as his reign progresses.
"We've identified the shortcomings and we'll address them with hard work. It was important to lay the foundations. In terms of attitude and the players' performance, we're on the right track."
The coach also rued Senegal's failure to make the most of their opportunities.
"There's disappointment because we always have that desire to win," Vieira said.
"But luck wasn't on our side. Maybe we'll convert those chances in the next match."
Senegal will face Ethiopia in their second qualifier in Bahir Dar on September 29 before playing Comoros in a friendly in Marseille on October 4.
Pitso Mosimane has made it clear that simply qualifying for the 2027 Africa Cup of Nations will not be enough for Bafana Bafana, with the new head coach setting his sights on continental glory.
Nigeria began their 2027 Africa Cup of Nations (AFCON) qualifying campaign with a nervy 2-1 victory over Madagascar in Uyo on Friday.
Angola coach Aliou Cisse was pleased with his side's disciplined performance after they held Egypt to a goalless draw in their opening Group B AFCON 2027 qualifier at the Cairo International Stadium on Friday.
Nigeria head coach Eric Chelle has named a 24-man squad for the upcoming 2027 Africa Cup of Nations qualifiers against Madagascar and Guinea-Bissau.
