The Blues were undone by two second-half goals from Sadio Mane.
But with a limited preseason to assimilate his new signings, Lampard believes there is still plenty of improvement to come from his team.
"Normally with new faces, you get a month or so of pre-season to work on your patterns of play and how you want to play so we have to have time. Every team that is successful in the modern day has had time and a process so now our process starts here.
"Last year was a squad where we couldn't do much business so we worked and worked to come fourth. Now it's a new start - our objectives are higher, our expectations are higher and that's fine. It will take some time but today I saw a lot of character and spirit."