The Midlands outfit are currently in 18th place, but are level on points with perennial battlers Wigan Athletic.
Lambert believes that teams like Sunderland, Newcastle United, Norwich City and Saturday's opponents Stoke City, who have not had to cope with the rigours of a relegation scrap for most of the season, may now begin to get nervous.
"For much of the season we've been accustomed to this situation," Lambert wrote in his column for the Birmingham Mail. "We've been living through it and we've dealt with the pressures it brings.
"Suddenly there are other teams that have been pulled into it, teams who haven't had to get their heads around it and we'll see now what happens. The important thing for us is that we don't get caught up in it all, that we continue to focus on our games, on our jobs and that's what we'll do.
"We've been playing well of late and if you can get on a little run we know how important it could be. The most important thing, however, is we are going into games with genuine vibrancy and a collective mindset to go and win."
Villa will close the gap on Tony Pulis's men to just one point should they win at the Britannia Stadium on Saturday.