Rangers, who have won the Scottish Championship title this season and will play in the Scottish Premiership during the 2016-17 campaign, got the better of Celtic in the last four of the prestigious cup competition in the month of April.
The tie finished 2-2 after extra time, and the Gers won the penalty shoot 5-4 to progress to the final of the Scottish Cup.
Mark Warburton’s side will be expected by many to compete for the Scottish Premiership title next season.
Griffiths, though, has suggested that Rangers should not read too much into their victory over Celtic.
“We will concentrate on ourselves and hopefully we can make it six titles next season,” the Scotland international striker told The Scottish Sun. “With Rangers, they have had a couple of bad results since they won their league.
“Okay, the beat us and managed to do that on penalties, so that was disappointing for us. They went through and we congratulate them, but next season will be a different ball game altogether.”
Celtic have the strongest squad in Scotland and are on the verge of winning the Scottish Premiership yet again this season.
The Bhoys are likely to make signings in the summer transfer window, and that is only going to enhance their chances of clinching the title next season.