The Europeans needed to beat Mexico to stand a chance of reaching the last 16, but a 3-1 defeat saw them exit the tournament early.
However, Kovac has told his players that they can be proud of how they competed during their brief stay in Brazil.
"The final score makes it looks worse than it really was though. Mexico were very compact at the back and we couldn't find a way through them," he told FIFA.com.
"We have to go home now, but life goes on. It's been a very positive World Cup for us, it gave us new impetus and we played well."
Croatia will now focus on their qualifiers for the 2016 European Championship, with their campaign getting underway at home to Malta on September 9.