Kroenke was speaking ahead of Sunday's win against Newcastle, which confirmed their place in next season's Champions League.
Kroenke said: "We plan to invest to get behind winning and doing better next season.
"We’re delighted we have our sporting director, Andrea, who will play an important role in this. He is part of a unified and strong team, supported by the board, who are crystal clear on exactly what we need to do and the way in which we want to do it. The right way. The Arsenal way.
"Ultimately, we all want the same thing. We’re as hungry for success as you are and that goes for everyone who works for the club. We have brilliant people right across Arsenal and I want to thank every member of staff for the dedication they have shown again this season. It’s something we have reflected on this week and it never goes unnoticed."
We've fallen short of targets
"As a club, we’re striving to win major trophies and, on the men’s front, we know we have fallen short of what we all wanted this season," Kroenke added. "Despite not reaching the Champions League final in Munich, our run to the semi-final of the competition still created some of our best nights this season.
"Our match here against Real Madrid was one of the best games and the most electric atmospheres we’ve experienced at Emirates Stadium. The game we played at the Bernabeu will no doubt live forever with those lucky enough to have been there.
"Mikel and his coaching staff, as well as the players, faced some challenges throughout the season and I want to give credit to the way they managed in these circumstances. It’s in these moments you learn the most."