Eckert led Saints on a 21-game unbeaten Championship run, with their only defeat in that spell coming against Manchester City in the FA Cup semi-final.
After beating Middlesbrough 2-1 on aggregate in the play-off semi-finals, Saints were expelled from the play-offs for spying.
Eckert has urged his players to recreate the form that left Saints one win from promotion.
“I think that there are moments to look back to that just excite you and that you just don’t forget,” Eckert told the Daily Echo.
“That is what it is about for us to generate those moments again.
“I’m very sure that we will be able to do that again and all of the challenges that come along the way; I think also the next season will have challenges for us.
“I hope that the bond that we have created, that we manage to strengthen that and then go forward.”
Eckert has had a hectic 12 months since joining Saints from Genoa as under-21s boss.
The 33-year-old took temporary charge of the first team in November before landing the job full-time and driving Southampton into the play-off places.
Last campaign then ended in disappointment and, during the off-season, the German became a father for the first time.
Asked if he had time to reflect on a whirlwind year, Eckert said: “I think that’s what the summer is there for.
“I think that the football club came off a very tough time. You don’t just turn that around easily and quickly. It needs a lot.
“Then it’s just one of the nicest things if you can bring some excitement back to a fan base that has suffered for a long, long time.
“And then obviously it hurts even more to fall the way we did towards the end of the season.”
