Two aspects - one easy, the other difficult; but both depend on the business of asking as 'a form of words'.
To the modern mind, words are just words. The idea of reciting some specific words to get a specific effect is not just obviously ineffective in everyday life, but ridiculous.
However, if we take seriously Owen Barfield's (and Rudolf Steiner's) idea that human consciousness has changed/ developed/ evolved through history (in accordance with a divine plan); then we should note that in Ancient Times it seems that 'merely' reciting words Did have a specific effect on the world. The 3,000 year Egyptian Empire was based on exactly this - which is why the magician priests (House of Life) were careful to keep their magical 'spells' secret - anybody who spoke them could use them, even without training.
Indeed, the written words did not (then) need to be spoken or read aloud. Egyptian spells might be carried around the neck in a container (phylactery) as a pendant, or dipped in a drink/ the drink poured over them - and then consumed, or written on the hand and then licked-off. The actual written words had an effect.
In terms of human consciousness this means that the words had objective power, words used-to constrain human consciousness - it was as if much of our consciousness happened outside of us, happened in the general consciousness of the group - and did not require awareness or intent. Men lived immersed in a group-mind, as part of a group-mind (not as separate sources of awareness and agency); and individuals (such as they were, which was 'not very' individual) were (mostly passively) influenced-by the group; which was itself continuous with the divine.
For us-now, almost the opposite is the case; and certainly words do not have objective power. So, the idea of 'asking' in prayer must be 'translated' for the modern mind. What it corresponds with - in modern consciousness - is that if we wish to live in accordnace with God's creation, we must consciously choose God's will. We must consciously ally ourselves with God.
So our mind needs to meet God's mind, our intent match God's intent; our prayer be in harmony with God's plans - for prayer to be effective. Yet harmony is not enough - we must still make a conscious choice to 'ask'.
On the one hand, God (obviously!) is not compelled to grant our every verbal request - we are no longer immersed in the group and divine mind as were the Ancient Egyptians; so our requests may be selfish and short-termist in a way theirs could not be. Nor does God impose his will upon Men, moving us around and compelling our thoughts as if we were puppets (or robots). For Good and also for Ill; Modern Man must consciously choose to do the right, follow the Good, live in harmony with God's creation.
It seems that extremely few people do this; indeed extremely few people even attempt to do it! Nonetheless from where we are now it is the only way forward (and going backwards is neither possible nor desirable).
The asking element in prayer can be considered a form of consciously chosen alliance with God. Obviously, we can only ask for what we can think, and we may be too corrupted (have too great a load of unrepented sin) to think in ways that are harmonious with God... In this instance, the asking in prayer, and the failure to meet a response to prayer, ought to be educational - ought to help us to clarify our own problems - ought to clarify that what we wanted and asked for is Not Good (i.e. not Good in terms of God's objectives, which primarily related to eternal resurrected Heavenly life). ...Not Good for us, and/ or not Good for somebody else.
But (here, now) Good things cannot happen without our active participation - and this is another aspect of the asking; of the need to ask. At this point (in this mortal earthly life) God needs us to participate-actively in his work; and if we don't participate with God (consciously, by-choice) then much of this work will not be done at all (since we will-not/ cannot be compelled or manipulated).
(Obviously, this failure to do our divine duty, failure even to acknowledge a divine duty to be done; explains some aspects of the extremely-bad spiritual state of the world: here, now.)
It is Modern Man's great privilege and duty to participate consciously with God. Privilege, because this was not possible to Ancient Man - immersed passively, as he was, in the group-mind - but also a duty, because necessary for God's work, here on earth. If we fail to do this duty, God's best (first choice) plans will fail.
(We have failed, God's first choice plans have failed, and second and third etc. choice back-ups - and we are now beginning to reap the consequences. Yet still we fail. Still we shirk our part.)
There-fore, I need to remember to ask: and ask with my conscious will, not just with words.