The warning was initially for his Disciples, but it has been relevant for every generation up until his second coming.
I would offer ."This generation" in Mathew above is the generation of the last days . The phrase "last days" is used in that way 8 times in the Bible. The pivotal point. . The time of reformation had come. The shadows of the ceremonial law became substance, the vail was rent. signaling the lasts days this generation .The last generation under the Sun.
.1 John 2 marks the last days as the generation that will not pass until the end comes ,the last day.
Little children, it is the last time: and as ye have heard that antichrist shall come, even now are there many antichrists; whereby we know that it is the last time. They went out from us, but they were not of us; for if they had been of us, they would no doubt have continued with us: but they went out, that they might be made manifest that they were not all of us.1 John 2: 18-19
Jude 17-19 King James Version (KJV) But, beloved, remember ye the words which were spoken before of the apostles of our Lord Jesus Christ; How that they told you there should be mockers in the last time, who should walk after their own ungodly lusts. These be they who separate themselves, sensual, having not the Spirit.