Villa had lost five straight Premier League games and were two points above the relegation zone when Gerrard quit Rangers to take over from Dean Smith, who was sacked in November.
The Midlands club have climbed from 16th place to 10th and will be bidding for a fifth win in seven league games under Gerrard against Chelsea at Villa Park on Boxing Day.
Gerrard said: “I had confidence and belief that we could come in and have the impact that we’ve had.
“The players deserve the credit for going and carrying those performances out.
“Once I started talking to Villa, the very first thing I did was look at the fixtures in the short-term.
“There were a lot of fixtures to be excited about, and I think the players have done extremely well in terms of the points return.”
Following Gerrard’s arrival, Villa have beaten Brighton, Crystal Palace, Leicester and Norwich, and have lost narrowly to title challengers Manchester City and Liverpool.
“We were close to taking a point out of the City game as well,” Gerrard said. “The Liverpool game was slightly different – they dominated for large parts.
“But I think we gave a good account of ourselves and made them extremely nervous in the latter stages of that game.
“The players should be confident, they should have loads of belief heading into a really busy schedule.”
When it was suggested the rest of the Premier League would now be treating Villa with more respect, Gerrard said: “Hopefully, and if it is it’s a compliment to my players.
“Since we’ve come in we’ve been extremely pleased with the level of performance, also with the points return.”
The former England and Liverpool skipper is aiming to make it 15 points from a possible 21 when his side take on Chelsea.
Gerrard added: “This is a game that we’re very much looking forward to and it’s a game we want to try and take some points from as well to set us up for the Leeds clash (at Elland Road on Tuesday).
“We’re excited and looking forward to the game on Boxing Day. We’ll go in and be as aggressive and ambitious as we can.”