Well, I will give you my interpretation of the passage you are referring to. You can judge for yourself if what I say makes any sense. He was comparing Himself there to the manna which the Jews were fed by the hand of God from Heaven, and the meaning is that Jesus was promising to provide for His own just as faithfully as God did with the Israelites in the wilderness:
30 Therefore they said to Him, “What sign will You perform then, that we may see it and believe You? What work will You do? 31 Our fathers ate the manna in the desert; as it is written, ‘He gave them bread from heaven to eat.’ ” 32 Then Jesus said to them, “Most assuredly, I say to you, Moses did not give you the bread from heaven, but My Father gives you the true bread from heaven. 33 For the bread of God is He who comes down from heaven and gives life to the world.” 34 Then they said to Him, “Lord, give us this bread always.” 35 And Jesus said to them, “I am the bread of life. He who comes to Me shall never hunger, and he who believes in Me shall never thirst. 36 But I said to you that you have seen Me and yet do not believe. 37 All that the Father gives Me will come to Me, and the one who comes to Me I will by no means cast out. 38 For I have come down from heaven, not to do My own will, but the will of Him who sent Me. 39 This is the will of the Father who sent Me, that of all He has given Me I should lose nothing, but should raise it up at the last day. 40 And this is the will of Him who sent Me, that everyone who sees the Son and believes in Him may have everlasting life; and I will raise him up at the last day.” (John 6:30-40)
When read in this context, it is less a promise about salvation as about provision, in that God faithfully provided for all the Israelites in the wilderness. Yet many of them turned against Him anyway, and so too was it clearly possible for the New Testament saints to as well. This is what Paul taught in 1st Corinthians:
10 Moreover, brethren, I do not want you to be unaware that all our fathers were under the cloud, all passed through the sea, 2 all were baptized into Moses in the cloud and in the sea, 3 all ate the same spiritual food, 4 and all drank the same spiritual drink. For they drank of that spiritual Rock that followed them, and that Rock was Christ. 5 But with most of them God was not well pleased, for their bodies were scattered in the wilderness. 6 Now these things became our examples, to the intent that we should not lust after evil things as they also lusted. 7 And do not become idolaters as were some of them. As it is written, “The people sat down to eat and drink, and rose up to play.” 8 Nor let us commit sexual immorality, as some of them did, and in one day twenty-three thousand fell; 9 nor let us tempt Christ, as some of them also tempted, and were destroyed by serpents; 10 nor complain, as some of them also complained, and were destroyed by the destroyer. 11 Now all these things happened to them as examples, and they were written for our admonition, upon whom the ends of the ages have come. 12 Therefore let him who thinks he stands take heed lest he fall. (1 Corinthians 10:1-12)
In this passage he is again talking about God's faithfulness to provide, and yet by verse 5 he brings up how they were nevertheless unfaithful to Him. So the overall promise of Christ in John 6 is that He will never leave us nor forsake us, and always provide for us the true Bread of Life so long as we keep trusting in Him and leaning on Him as our provision. If we do not, however, the same fate can befall us as befell the Israelites in the wilderness.