The Glasgow giants easily won their third straight Scottish Premiership this term but fell short in both the Scottish Cup and League Cup while failing to get past the group stage in Europe's premier club competition.
Celtic have been extremely difficult to beat in the league this term, losing on just one occasion, but Nigerian defender Ambrose feels they can now take form that into both cups competitions and the Champions League in 2014/15.
"If we get things right I don't think anyone can get close to Celtic," he told the Daily Record.
"The league is getting better and teams are trying to compete with us. So the more they try to compete, the more we will try to step up.
"We will become better players because we know there will be a challenge in the league.
"To keep winning you have to do the right things and have the winning mentality. You need to have the right players and manager - everyone needs to be together.
"We have to aim for the Treble and to do better in the Champions League. I think we have the calibre of player to do that.
"Last season we won the Double and this year we have just one trophy.
"The Treble is what is left for us to achieve and that is the motivation next season."
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