His team had earlier crushed Werder Bremen 5-0 to open a 16-point gap over deposed title holders Bayern Munich with five matches left in the season, securing their first trophy in 31 years amid wild celebrations from a 30,000 home crowd.
"We wanted to play games with a good mentality this season and the players quickly started working well together. After the first few matches we saw this team can play really good football," Alonso told a press conference.
"But to achieve this in such a way was a top performance. Finally, it is an honour to say that Leverkusen are champions. It is totally deserved for the team, fans and the club."
The Spaniard, who took over in October 2022, can win more titles this season with his team also through to the German Cup final and the Europa League quarter-finals.
"It is a big success for the club. The first time is special for everyone. We can say we were part of this big day for Bayer Leverkusen. It feels great," said Alonso, who will stay on at the club despite major interest from top European teams.
Leverkusen are on a 43-game unbeaten run across all competitions and have further extended the longest unbeaten streak in a single Bundesliga season to 29 matches.
"We did not talk much about the title in the changing room but it was in our heads that this year we could be champions," said Alonso.
"Now we must enjoy the moment. It has been a totally intense season so far and it is not yet over. We cannot forget it."
"Now this is behind us and we still have big goals this season," he said before the players stormed into the room showering their coach with beer.
Leverkusen travel to West Ham United next week for their Europa League return game after a 2-0 first-leg victory.
