Chelsea manager Jose Mourinho was victorious for the first time in five attempts at Villa Park on Saturday, as full-back Ivanovic's wonderful left-foot volley in the 66th minute secured a 2-1 win.
With Manchester City having only drawn 1-1 with Hull City, leaders Chelsea stretched their lead to seven points at the top of the table.
Ivanovic, though, was quick to stress that the London club can ill afford to rest on their laurels.
"We cannot be relaxed. This is a massive three points for us," he told Chelsea's official website.
"The game was very tough but at the end of the day I think we deserved three points.
"We don't have time to relax even one second. There are 14 games to go and we must stay focused. Seven points is big but this can change quickly."
Chelsea are back in Premier League action on Wednesday, when they welcome Everton to Stamford Bridge.
'Will Cristiano Ronaldo and Neymar extend their contracts in Saudi Arabia? We play a facilitating job, but it’s down to the players and the clubs to decide' Saudi Pro League chief reveals how talks will work for out-of-contract duo
Nations League: Who are the ITV commentators and pundits for England vs Republic of Ireland?
