I would say yes. We are his children and the natural relationships we have on this earth should reflect the relationship God wants with His children. If we, as parents, spouses, friends, etc don't like to hear others criticize themselves, then I would say God does not either.
He sent His Son to this world to die for us. John 3:16-17 says For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
When we have taken on the Name of Jesus through salvation, we are no longer our own. We are His. We are filled with His Spirit and are a temple of the Holy Ghost.
What? know ye not that your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own? For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's.
1 Corinthians 6:19-20 KJV
God sees us as His, as chosen, and as precious.
But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:
1 Peter 2:9 KJV
And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight:
Colossians 1:21-22 KJV
We have been reconciled so He can present us holy and blameless. When we talk down to ourselves, we may be insulting the very work God has done in us. Yes, we need to humble. Yes, we need to be aware of our sinful nature and make sure we are not allowing sin and pride to rule. Yes, we must examine ourselves and make sure we are right with God as it says in 1 Corinthians 11:38. But, that does not give us permission to tear ourselves down and destroy what God has given us. As a child of God we must know who we are and walk as such. We must recognize the Spirit working in us. We must realize that God's love and mercy applies even when we mess up, make a mistake, and need a little grace extended even to ourselves. We should not discount who we are in Christ. How we talk to and about our own self is important. If I continually view myself as worthless, no good, and can't do anything right, we are not placing ourselves in a position of servanthood to Christ. We are not in the right mindframe to be used, to hear from Him, or to even be available to Him. We cannot be self loathing and reflect the love of God to others. This will destroy us rather than lead us to God. The enemy uses our mind to work against us and what God wants for us. If we allow our own thoughts to keep us from listening to God, from working for Him, we are allowing the enemy to win out. I dare say, we are working against God in this manner. God has not called us to condemn ourselves. He called us to live and be free.
But now being made free from sin, and become servants to God, ye have your fruit unto holiness, and the end everlasting life.
Romans 6:22 KJV
We need to put on a new mind when we are redeemed. We are to change our thoughts as well as our words and actions to bear the fruit of His Spirit.
That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts; And be renewed in the spirit of your mind; And that ye put on the new man, which after God is created in righteousness and true holiness.
Ephesians 4:22-24 KJV
I encourage us all to consider our thoughts not only about others but how we think of ourselves. God may trying to talk to you and show you things He sees for us, but we may be too busy tearing down what He has tried to build up. Knowing who we are in Christ, believing His Spirit is working in us and through us, and realizing we are His anyway, may just change our lives, our ministry, and our relationship with Him and others.
Casting all your care upon him; for he careth for you.
1 Peter 5:7 KJV
We can place those cares on Him. He cares about us and takes our burdens. We need to recognize our value to Christ. We are precious in His sight. He believes in you. We need to believe in us too. He believes we are more than conquerers, we are blood bought, we are forgiven, and a temple of the Holy Ghost. Let us believe that He who made us, saved us, and called us, also needs us to believe it and act like it.
