Alonso secured his fourth podium of the 2023 season in last weekend's Miami Grand Prix after claiming a front-row starting spot, just losing out to an unstoppable Red Bull 1-2 led by Max Verstappen who won the race from ninth.
His fourth podium in five races prompted the Spaniard to start aiming even higher, even if Aston will need Red Bull misfortune to challenge for wins.
"I think at the beginning of the year a podium was amazing. Now after four podiums we want obviously more, and at least a second place," Alonso said.
"But the two Red Bulls are always unbreakable, and they are always super-fast. But maybe Monaco, maybe Barcelona we have a possibility."
Team boss Krack urged the team to stay realistic and says it will not take its current run of podiums for granted given the level of competition from Mercedes and Ferrari.
"Feet on the ground, you should never take a podium in F1 as normal or as a given," Krack replied when asked if podiums are starting to feel normal for the team that finished seventh in the 2022 championship.
"It's a lot of hard work involved to be on the podium and you have very, very strong competitors in Formula 1, very professional.
"And if we are not 100% in all areas at all times, then there is no podium."
Rather than trying to catch Red Bull, Krack acknowledged his squad would do well to hang on to its shock second position in the standings.
Ferrari has shown excellent flashes of one-lap speed but is struggling for consistent race pace, meanwhile Mercedes is bringing an all-new sidepod, floor and front suspension to Imola's Emilia Romagna Grand Prix in two weeks' time.
If both squads manage to make substantial steps forward, then Aston is facing a big task to stay in front with still 18 rounds left to run. Despite its woes, Mercedes only trails its customer team by six points.
Looking forward to a gruelling triple-header with Imola, Monaco and Spain, Krack said: "It will be very hard for man and machine because it's three weekends in a row.
"You have Monaco in the middle, which is logistically very, very difficult.
"Everybody will bring stuff, we will bring stuff. So I think this will add a little bit of extra work to everybody in terms of understanding what you have done in terms of putting the parts on.
"It will be quite challenging, but we're looking forward to it."
