All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Making Athkaar is not a condition for the validity of the rounds of Tawaaf. It is merely recommended to make Athkaar while circumambulating the Ka‘bah. Some scholars provided as proof the Hadeeth that is narrated on the authority of ‘Aa’ishah where she stated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Tawaaf around the Bayt (Ka‘bah), (Sa‘y – walking)) between As-Safa and Al-Marwah, and throwing pebbles were only enjoined to establish the Remembrance of Allaah.” [Ibn Khuzaymah and others, Al-A‘thami: Authentic chain of narrators, Al-Albaani: Weak]
As it is made clear that it is recommended, not conditional, to make Athkaar to maintain the validity of Tawaaf, you did not have to repeat the two rounds, since your first Tawaaf was valid anyway.
Allaah Knows best.