After the Hammers held Mourinho's Chelsea to a goalless draw in January, the Blues boss accused Allardyce's side of playing "football from the 19th century".
Asked about the criticism ahead of West Ham's return to Stamford Bridge, Mourinho described the comments as "silly words".
Allardyce highlighted the draw as the turning point in their season, and survival last term has turned into something much more impressive this campaign.
West Ham beat Leicester 2-0 last weekend to ensure they reached Christmas in the top four for the first time since the 1985-86 season, when they ended up finishing third.
Mourinho has been more impressed with the Hammers than any other team besides his own and has no doubt Friday's match will be very different to last season's.
He said: "Chelsea is top of the league and deserves it and after us West Ham, because to be fourth for a team that everybody was expecting them to fight for survival, I think is a fantastic achievement.
"Both teams are different than last season
We are a better team, we have more creativity and more goals, we have more attacking dynamic, and West Ham is also a better team.
"Last season they were in big trouble
When you are fighting against relegation, you have to do everything to get points.
"Yes it was a turning point for them because it gave them the confidence they needed and after that they kept in the division
This team is different.
"You see the way they play every game, they are a better team, they have better players and I think also Big Sam is showing now he is not what people sometimes say - a defensive coach, only knows how to play defensively and direct with long balls.
"He is giving a completely different image about himself, which can make the game more difficult for us but at the same time more attractive for everyone.
"He has my respect
Last season I had a couple of words about the fact they started winning time after two minutes of the game, which I don't like.
"But I respect him as a coach
As a person he's a very good guy, but as a coach he has a beautiful career and I'm very happy that he's doing well with West Ham."
Mourinho and Allardyce may seem unlikely bedfellows but the Portuguese revealed the pair bonded during their involvement at a charity match during the summer.
"We exchange lots of messages," said Mourinho
"We have a good relationship.
"Me, him and Peter Reid were together for one week for the Robbie Williams match in the summer, Soccer Aid, having lunch, having dinner.
"You get a different kind of relationship, you know the person much better, which you can't do when you just play against each other, see each other for one minute before and after the game
I like him very much."
West Ham are still big outsiders to finish the season in their current position, but Mourinho does not believe it is impossible.
He said: "If they finish top four - manager of the season, Big Sam; team of the season, West Ham; because it would be an amazing achievement comparing West Ham with the investment other teams had to finish in the top four
Why not?"
Source : PA
Source: PA