The head coach said his players are now playing much more effective football on the pitch
The Blaugrana made it five wins out of five Champions League matches with a comfortable 3-0 victory over Ferencvaros in Champions League Group G on Wednesday.
Barca will have the chance to win all six of their group games for the first time since the 2002-03 campaign when they face Juventus at Camp Nou next Tuesday.
Koeman’s side have struggled in La Liga this season, though, and are 12 points behind leaders Real Sociedad – albeit with two games in hand – after losing three and drawing two of their opening nine games.
The Dutchman, however, suggested there has been a significant difference in the performances produced by his players in recent weeks.
It was emphasised by Barcelona’s stylish second goal, scored by Martin Braithwaite, which featured a sequence of 33 consecutive passes in the build-up – the most for a goal scored in the Champions League this season.
“Lately, we have more effectiveness,” Koeman said in a post-match media conference. “In defence we can still improve, but we are on the right track and hopefully we can continue like this.
“The difference is the team has been effective in the games. It is quite a big change compared to the beginning of the season. The hunger that we have, you have to prove it.
“The most important thing is to get to the last 16 of the Champions League, but if you win six out of six it would be a historic milestone.”
Barcelona’s win in Hungary was secured thanks to additional goals from Antoine Griezmann and fellow France international Ousmane Dembele, who netted from the penalty spot.
Koeman was particularly impressed with an eye-catching performance from Dembele.
The 23-year-old was a menacing presence on the left flank and attempted five shots, more than any other Barca player.
“Dembele is a great player,” added the Barcelona head coach.
“He is very fast, he plays with both legs and is physically very well. For the coach it is difficult to make decisions when people like Dembele are playing as they are.
“There is a lot of competition in attack. You can see that we have a good squad and we have been able to let several players rest.
“Those who have played have shown that there is competition, and want to play well and create chances.”