Downing signed a four-year deal at Upton Park on Wednesday, after a £6million deal was reportedly agreed between Liverpool and the London club.
The winger struggled during his two-year spell at Anfield, scoring seven times in 91 appearances, and Allardyce is hoping to see the 29-year-old recreate the form he showed at Villa Park, where he hit 11 goals in 79 games, assisting a further 13.
"I think that I was more (interested in) Stewart Downing (at) Aston Villa than I was Downing (at) Liverpool," he said. "I think that Downing, at Villa, was more what I'm looking for than perhaps he was at Liverpool.
"That's no reflection on what Stewart did at Liverpool, because he was asked to play a different way than he was at Villa.
"As everybody knows I love crosses and equally, there are lots of people who don't like crosses anymore."
Allardyce has added five new players to his squad ahead of the new campaign, and while he is confident ahead of the opening day clash with Cardiff City, he knows it will not be an easy game for his side.
"I think that Malky (Mackay) has gone and invested in his team and they will come all guns blazing," he added. "Like every other team that gets promoted, particularly the team who win the league, the enthusiasm carries over into the early part of the Premier League season.
"Complacency is certainly not what we're after. The perception outside of Cardiff and West Ham fans is that we're going to turn up on Saturday and win easily.
"My message to the lads is that there's no easy game in the Premier League and if we don't hit the ground running and hit our top form, this will be a very difficult game for us."
