Je n'ai pas dû bien regarder

Apart from the standard auxiliary verbs in compound tenses/moods - those using être or avoir as true auxiliary verbs - other dual and multiple verb constructions in French consist of the first (or semi-auxiliary) verb in its appropriately conjugated form, followed by the other verb/s in the construct in infinitive form (which includes the use of the infinitive passé).

 In your example ‘ai dù’ the conjugated verb devoir in passé composé (setting the tense), and the following verb in the ‘verb grouping’ in the infinitive - regarder.

 

 Tu vas courir ? - You are going running ?

Tu vas le laisser tomber - You are going to drop it/let it fall. 

Tu l'as laissé tomber - You dropped it/let it fall. 

 

Here is one link covering this, and other advanced uses of the infinitive :

https://www.fluentu.com/blog/french/french-infinitive/