Context is everything in looking at this result.
Fans aren't celebrating being out, nor are they apathetic towards the FA Cup. If we were sixth in the league, I'd want us gunning for a FA cup. If we were out of the CL and league contention, I'd want us gunning for the Europa League and FA Cup.
But we're not. We're trying to win the league against one of the most expensive and talented sides ever assembled and we're still in the Champions League. Accumulated fatigue and injuries will be our biggest hurdle in winning either of these competitions and ergo the second string will (no, has to) play in the domestic cups.
Wolves away is a tough game this season with a full strength team so I'd reconciled myself to a cup exist if using the second string. And look at what our reward for a win probably would've been: a cold dark night in Stoke sandwiched between Palace and Leicester (who will have no FA Cup distraction) in the league.
City could well win 2 domestic cups, but to do so they'll have to play eight more games than us this season*, and that does take a toll on fatigue and injuries regardless of how good your side is.
Let's also think of the money, because while not romantic, it's important. Playing four more games in the FA Cup and winning it gets us less money than getting past Bayern will. It would take us to win over 10 FA cups to get the same money as you get from winning one CL - and there's no need to mention the prestige of one over the other. Last year we got over £72m for our CL run, this year's FA Cup winners will get around £6.5m (incidentally, the same amount we'll get for our next 4 games in the CL).
There's also the question of; if we don't play our youth and second string in the cup, when do they get to play? Our young players will have learned so much from the game last night, regardless of the result.
*CL not factored in.