Even if we can’t render full service, the Lord understands and accepts

If a devotee sincerely surrenders, the Lord, as the Supersoul in everyone’s heart, immediately understands this. Thus even though, externally, a devotee may not render full service, if he is internally sincere and serious the Lord welcomes his service nonetheless. Thus the Lord is known as bhava-grahi janardana because He takes the essence of one’s devotional mentality.

Srimad Bhagavatam 8.23.2 purport