Croatia were made to work against minnows Malta, despite having a numerical advantage after Steve Borg was sent off in the 31st minute of their Group H encounter in Zagreb on Tuesday.
The hosts failed to make any inroads during the first half and it was not until the 46th minute that the deadlock was broken by birthday boy Luka Modric.
Andrej Kramaric - earning just his second cap - sealed the points nine minutes from time in the Croatian capital.
While Kovac was satisfied with the win, the 42-year-old said he is hoping to see his side reduce their errors.
"We met our target. We have three important points to start off qualification," Kovac said.
"We shall analyse the match, maybe to see where we made some mistakes, particularly in the first half. I will not single out anyone - the whole team gave their best.
"Congratulations to everyone. My players are eager to play matches. They are getting better and better.
"The goal is to play an entire 90 minutes well. Maybe against Malta it was not the case, but that is the goal."
Modric, who celebrated his 29th birthday and 80th cap in style, ended his international goal drought.
The Real Madrid midfielder had not scored since Croatia's 3-1 victory over Israel in September 2011 but he played down the goal.
"It was not an easy match for us, it was difficult. Malta were defending very well, even when they were down to 10 players," Modric said.
"But we opened the second half with the goal and that made our job much easier. At the end we could have scored more goals, but the victory is the most important thing.
"I scored my first goal after three years for the national team, but it is not a relief now, why it should be a relief?"
