Did the Buddha state that there is only one way, and state/imply that any other path (such as those practiced by yogis) was futile? This question mainly came up to my mind as I thought about how interconnected some concepts and practices of Buddhism are with other spiritual practices, such as meditation, and the concept of letting go. 

Was the Buddha ever questioned about something of this nature, and did he ever make this clear at any point in his teachings?
https://suttacentral.net/en/mn11 for the Buddha's statement that there are no true recluses beyond the Sangha. 


  “Bhikkhus, only here is there a recluse, only here a second recluse,
  only here a third recluse, only here a fourth recluse. The doctrines
  of others are devoid of recluses: that is how you should rightly roar
  your lion’s roar."


The Buddha is careful not to deny the achievements of others, but framing achievement through the understanding of the four kinds of clinging, he implies that others may reach a very close goal, yet through having wrong view with regards to Self, through not penetrating anatta, are still clung to it, and hence have not cut off clinging (and therefore craving, which correlates directly with suffering) at the root, when declaring so. 


  "Bhikkhus, there are these four kinds of clinging. What four? Clinging
  to sensual pleasures, clinging to views, clinging to rules and
  observances, and clinging to a doctrine of self.
  
  Though certain recluses and brahmins claim to propound the full
  understanding of all kinds of clinging, they do not completely
  describe the full understanding of all kinds of clinging. They
  describe the full understanding of clinging to sensual pleasures
  without describing the full understanding of clinging to views,
  clinging to rules and observances, and clinging to a doctrine of self.
  Why is that? Those good recluses and brahmins do not understand these
  three instances of clinging as they actually are. Therefore, though
  they claim to propound the full understanding of all kinds of
  clinging, they describe only the full understanding of clinging to
  sensual pleasures without describing the full understanding of
  clinging to views, clinging to rules and observances, and clinging to
  a doctrine of self.
  
  Though certain recluses and brahmins claim to propound the full
  understanding of all kinds of clinging…they describe the full
  understanding of clinging to sensual pleasures and clinging to views
  without describing the full understanding of clinging to rules and
  observances and clinging to a doctrine of self. Why is that? They do
  not understand two instances…therefore they describe only the full
  understanding of clinging to sensual pleasures and clinging to views
  without describing the full understanding of clinging to rules and
  observances and clinging to a doctrine of self.
  
  Though certain recluses and brahmins claim to propound the full
  understanding of all kinds of clinging…they describe the full
  understanding of clinging to sensual pleasures, clinging to views, and
  clinging to rules and observances without describing the full
  understanding of clinging to a doctrine of self. They do not
  understand one instance…therefore they describe only the full
  understanding of clinging to sensual pleasures, clinging to views, and
  clinging to rules and observances without describing the full
  understanding of clinging to a doctrine of self."


With regards to the way to the goal, since the purpose of recluseship at the time was to comprehend experience (stress/suffering) as it actually is, with direct insight, there will only be one correct answer. In a world of anicca, anatta follows naturally, unless one relies on a transcendental (beyond experience) notion of Self. Therefore, the above quote is a fair statement. 

https://suttacentral.net/en/mn26 The Buddha himself had two teachers to whom he went to before his enlightenment, Alara Kalama and Uddaka Ramaputta, who came very close to cessation in meditation, but not having the insight into impermanence, could not arrive at the true cessation of suffering. 

Patanjali states that 'The restraint of the modifications of the mind-stuff is Yoga.', which is the cessation the Buddha practiced (the ceasing of mental fermentations). However, Patanjali then infers a transcendental notion of Self (I assume it is implied that once modifications to the mind cease, the True Self is said to be left), which, if it is to Be, is logically beyond conditioned experience as it is an independent entity, and hence not verifiable in the here and now. Such a position naturally creates doubt and does not lead to final release. 

The only path within Buddhism is the Noble Eightfold Path, which encompasses right view, right intention, right speech, right action, right livelihood, right effort, right mindfulness and right concentration. Yogis may be accomplished in many of these and that would be a great attainment for them and their students, but all other than the Buddha stumbled at right-view - the first step, because they conceived of their notions of Self.