The German champions take on Atalanta in the Europa League final in Dublin on Wednesday before facing second-tier Kaiserslautern in Saturday's German Cup final.
Leverkusen made Bundesliga history by romping to their first ever title without losing and are yet to taste defeat in 51 games in all competitions this season.
"What matters above all tomorrow is mentality," said Alonso at his pre-match press conference on Tuesday.
"We have a gameplan but the players still have that wonderful atmosphere from the title celebrations on Saturday and we want to tap into that."
Alonso's success in less than two years in his first senior managerial role has made the former midfielder Europe's hottest coaching talent.
The 42-year-old has rebuffed the interest of former clubs Liverpool and Bayern Munich to remain in charge at the BayArena next season.
"I was so young in this coaching career when I was offered the Leverkusen job so it was 'let's go, let's see what happens'," he added.
"It has only been a year-and-a-half but we have made so many right decisions. The mentality we have shown throughout the years has been fantastic."
Yet, it is the one major disappointment of his time in charge that Alonso hopes will serve as extra motivation in the Irish capital.
Leverkusen lost 1-0 on aggregate to Roma in last season's semi-finals.
"Losing in last season's semi-final is a huge motivation; we have already spoken about how things felt last season," said Alonso.
"We were very close to the final. We have harnessed this disappointment to our benefit.
"When you go to the final you don't go there to make up the numbers, you go to win it. We will try and make one last effort."
Granit Xhaka has been one of Leverkusen's revelations since joining from Arsenal less than 12 months ago.
The Swiss midfielder rejected the suggestion that his side have nothing to lose after winning the club's first ever league title.
"I do actually think we have something to lose, absolutely," said Xhaka.
"You go into finals to win them. Our primary goal was to win the Bundesliga and our secondary goal was to win this.
"We will do all we can to come back to Germany with the trophy."
Alonso confirmed that Europa League regular Matej Kovar will start in goal rather than captain Lukas Hradecky.
Star forward Florian Wirtz also looks set to start for the first time in nearly a month after recovering from a muscle injury.
