The Portuguese coach said over the weekend he expected a "difficult" season if no-one else came in but seemed to backtrack ahead of Friday night's Premier League opener against Leicester - and went on to suggest finishing second last season is among the highlights of a career that has been littered with domestic and European success. United said they were happy to be kept informed.
But Allardyce has some sympathy for United's chiefs, given the prices they were quoted for various players.
Last season may have been United's highest finish since Sir Alex Ferguson retired but the 19-point gap to runaway Premier League champions Manchester City underlined the improvements required. New signing from Dinamo Zagreb, Filip Benkovic, does not stand a chance to feature after having to still train with his new teammates. Man. United 2, Leicester City 0.
The club did not consider any other centre-back on Jose Mourinho's wishlist of a similar value. Paul Pogba, Marouane Fellaini, Ashley Young and Jesse Lingard return to training after extended leaves on Monday, which means that they are likely to be unfit for the match.
However, Tottenham have become the first Premier League club not to sign a player since transfer windows were introduced in 2003, with their primary target Jack Grealish remaining an Aston Villa player. "I'd prefer to look to the bench and to have them rather than to have 16-year-old boys without experience and without the power to be Premier Leagues players directly", said Mourinho.More news: Chelsea prepared to beat Liverpool to the signing of £53m attacker
"It is hard for me to understand, to feel, to believe we finish second - which I keep saying, and it is sometimes hard to believe".
There was no question of Pogba being allowed to leave and there remains great support for Anthony Martial at the club, with every inquiry about him over the summer being met with a firm refusal.
"No miracles", he told a press conference (via United's official website).
"A lie repeated 1,000 times is still a lie, but the perception of people is that it's true". "I like to work with my players".
Sanchez signed for United in January, and has so far struggled to replicate the goals and attacking threat he consistently displayed during his three-and-a-half years at Arsenal. It gives us a couple of weeks to recover people and to prepare people better and to focus on the players that are available, so I'm not even thinking about that list of players I gave you - Matic, Valencia and so on.