Sword of Spirit
Legend
The warlock is never going to be a top tier class on its own. There are fun things to play, you've got lots options, but its always going to have issues keeping up in damage, and there are still a lot of trap spell options. This doesn't change at high level.
(Now, I'm going to assume you are not comparing warlock's at-will damage to fighter or barbarian, intentionally the best of the best. Since his at-will damage is as good or better than everyone else, I'm guessing you are referring to his damage compared to a wizard or sorcerer.)
With that said--I'm not seeing it.
I ran some numbers. I compared the damage over an adventuring day of a warlock with a sorcerer and wizard at 11th level. Based on 6-8 encounters per day, and about 3 rounds (or less) per encounter, I assumed 18 rounds worth of battle. I didn't take into account any feats, any damage over time spells, any hindering effects, etc. Since the question is about a warlock's damage, I went purely for blasting spells (and a hex for the warlock).
I ran both damage dealing optimized (fiendish warlock, draconic bloodline (fire), evoker) and any old versions of each class. I ran calculations for including extra damage on area of effects according to DMG estimations of how many targets an area effect spell would hit, and I ran calculations if we assume blasting a single target only. I assumed that attack rolls hit 50% of the time (and therefore halved average damage on attack spells) and assumed saving throws were made half of the time (for 75% damage on save spells). I attempted to make optimal choices amongst blasting spells, including casting lower level spells in higher level spell slots if it was advantageous for that specific calculation, focusing on spells that would benefit from class features, and using Arcane Recovery and Sorcery Points to create the best possible spell slots. (One thing I did not do is mess around with Twinned Spell. It is possible that could have made a difference for the sorcerer in the single target calculations). I rounded down all fractions.
Here are my results for damage over an adventuring day for 11th level blasters.
With area effect damage included:
Wizard (Evoker) 1621
Sorcerer (Draconic) 1435
Wizard 1314
Sorcerer 1308
Warlock (Fiend Pact) 1281
Warlock 469
Single target damage only:
Wizard (Evoker) 751
Warlock (Fiend Pact) 458
Warlock 450
Sorcerer (Draconic) 370
Wizard 343
Sorcerer 333
So what we can see is that the evoker wins against anyone, anytime--provided he uses all 18 of his spell slots (including Arcane Recovery) just doing damage. (It worked out so that the sorcerer and wizard exactly used up their spell slots and never had to fall back on their inferior cantrips).
The draconic (fire) sorcerer beats the standard wizard, provided he uses all of his spell slots and Sorcery Points for blasting.
The warlock comes in dead last when it comes to area effect damage. However, note that in the case of the Fiend Pact warlock his damage isn't that far off from the sorcerer. The difference is probably insignificant.
When it comes to single target damage, we see something quite different. The evoker is at the top, but only because magic missile works weirdly (he adds his Intelligence modifier to each missile), making it crazy good for an evoker. If it were only added once, the damage would be more like 415--placing it above the sorcerer but below the warlock (regardless of pact--which makes little difference for single target damage).
Without the evoker shenanigans, the warlock is the clear leader on single target damage. That's where he shines in the damage department. His at-will attacks make up for his lack of spell slots: over half of his attacks were actually with his eldritch blast.
And that's just damage. After using up their spell slots, wizard and sorcerer have very few resources left except cantrips (and rituals for the Wizard) while the Warlock has plenty of cool invocations to let him mimic spell effects and gain unique non-combat abilities all day long (as well as having cantrips, and even better access to rituals with the right Pact Boon).
Warlock is not weak. It is different, but it definitely seems to work as intended: excelling in single target damage, while boasting a suite of mostly at-will abilities for a wide variety of situations.
(And anyone who cares more about balance than I do might want to reject the official ruling on magic missile to keep the evoker from leaving all other casters behind in damage.)