Gerrard marked his 650th appearance for the Merseyside club with a goal from the penalty spot in a pulsating Premier League clash on Sunday.
Luis Suarez scored twice to take his tally to 22 goals in just 16 top-flight games this season, while Daniel Sturridge marked his return from injury with a goal as Liverpool secured their first league win at the Britannia Stadium.
The Reds let a 2-0 lead slip earlier in the game but Gerrard was impressed with the manner in which his team responded to Stoke's fightback to secure the win, which ensured they regained fourth place from Everton.
"I thought we showed tremendous character," the 33-year-old told Sky Sports.
"For the first 40 minutes we controlled the game, were very comfortable and were 2-0 up - and then we made a couple of mistakes. It became a real tough game from then on.
"It was big because our record against Stoke in the Premier League is poor away from home, so we wanted to put that right today.
"Today was all about the team performance and the three points, and it's results like these we need if we want to finish in the top four."
The England skipper was making his first start since returning from a hamstring injury, and he knew Liverpool could ill afford to drop points against Mark Hughes' men.
"I was disappointed to get the hamstring injury, but it was great to be back with the lads and it's all about the top four now - not personal achievements, goals or appearances. We just wanted to get back in that top four," he added.
"Results went against us yesterday and put even more pressure on us today to get a result, but the lads were fantastic."