West Ham came close to completing a loan move for the Togolese, who is likely to be consigned to the bench when the Hammers travel to face their London rivals at White Hart Lane on Sunday, on the final day of the January transfer window.
Adebayor has played just three times for Spurs since their defeat to Stoke on November 9 and has also been the recipient of jeers from home fans during that time.
Although he is one of Mauricio Pochettino's three captains, the Argentinian would not have stood in the way of Adebayor leaving the club in January - with suggestions chairman Daniel Levy was the man who vetoed a loan deal to rivals West Ham.
That leaves the 30-year-old as part of Pochettino's squad but, with Harry Kane in fine form, first-team opportunities are still likely to remain at a premium for Adebayor, although Allardyce admitted he would have relished the prospect of working with the former Arsenal and Manchester City man - despite his reputation for causing unrest.
"Goals," was Allardyce's simple reply when asked what the signing of Adebayor would have brought to West Ham.
"If you see where he has gone and his initial impact at where he has been would be that he comes into a football club and scores goals on a regular basis.
"There is obviously one of those players that you have to look at him and as a manager and say 'how do I react with him and interact with him and on the basis of how well I interact is on the basis of how well he plays for us'.
"So you use your management skills in terms of looking at his personality, like you do with most players and talking about wanting the best out of him while you are here, and wanting him to enjoy your football and do what you do best - play and score goals.
"I never really think I have anybody signed until I know they are at the training ground at the final pieces, however long, or short the contract is
It looked a really good possibility but I was keeping my fingers and toes crossed.
"If you are in the transfer window and a quality player comes your way and you think he is a quality player, some people say 'do you need a player in that position?' - but the bottom line is that he is a quality player.
"If you can get him, for me you get him if you can afford him
That is what we tried to do
There was such a short time frame at that time it was not possible to be pulled off."
Any frustrations at not getting a last-minute deal for Adebayor over the line on transfer deadline day would have been magnified when club-record signing Andy Carroll was ruled out for the remainder of the season after undergoing knee surgery.
Allardyce conceded Adebayor would have been the perfect fit to step in with Carroll sidelined but has now called on the likes of Enner Valencia, Carlton Cole, Diafra Sakho and new arrival Nene to prove their worth.
"Any player with the ability that he has got is my kind of player," he added of Adebayor.
"Particularly with a relatively good goalscoring record
There can be the odd blip that happens with a player of his character but sometimes you deal with that as a manager.
"You don't want it to be easy week in and week out
you want some challenges
You set yourself the challenge that you hope he can make a difference to your team
But it was not to be.
"We have players here that have got to perform from now to the end of the season
There is no let up.
"They can't take it easy and sit back on what they have done in the past and they have got to continue to strive for the future and hit the levels we have performed at for most of the season."
Source : PA
Source: PA