After Robert Andrich gave Leverkusen the lead, Bayern's Aleksandar Pavlovic levelled with a stunning half-volley from 25 metres out which beat goalkeeper Lukas Hradecky to leave the visitors third in the standings.
Bayern had 18 shots to Leverkusen's three but despite the home side having nearly 70% of the possession, Alonso's team managed to take home a point as the Spaniard extended his unbeaten record against the German giants to four games.
"The energy and belief at Bayern is different than last season, they are going full throttle with and against the ball. That was very tough today. We can be happy with the point," Alonso said after the match.
"I needed more energy from the team, I'm happy with that. We were ready to suffer and we did that. We need the discipline and passion of the players.
"It wasn't easy, we didn't have control of the ball. It was a challenge to defend. The point is important... The whole team did very well. We hardly had a chance to breathe but I'm very proud of my players."
Leverkusen midfielder Granit Xhaka, who provided the assist for the opener, said their main strategy was to be compact and deny Bayern opportunities to score.
"We are self-critical. If you score three goals every game, that's not enough. If we play well today and switch gears, we can do something," Xhaka said.
"Defensively, we put in a good performance. The goal today was to be compact and concede little. You can certainly do more with the ball and everyone knows that we can do more.
"If someone had told us before the game that we would get a point, we would have taken it."
Leverkusen will next turn their attention to the Champions League where they host AC Milan on Tuesday.
