The Reds have not participated in Europe’s elite club competition since the 2009-10 season, and have spent two of the past three campaigns outside of European competition altogether.
However, the England skipper now believes his side have turned a corner and grown in character, confidence and capability.
"If we'd gone 2-0 up there a few years back we'd have probably lost the game 3-2 after letting Stoke back into it," said the midfielder.
"The manager asked us at half-time if we had the character and bottle to go and win the game and we went and proved we can.”
Liverpool's next five League games
- 18 Jan: Aston Villa (H)
- 28 Jan: Everton (H)
- 2 Feb: West Brom (A)
- 8 Feb: Arsenal (H)
- 12 Feb: Fulham (A)
Sunday’s victory at the Britannia Stadium was Liverpool’s first win at Stoke in almost 30 years, and the 33-year-old believes such results prove Brendan Rodgers’ side are a different prospect this season.
"We feel as if away from home we can click and get that consistency and we can add that to our home form we are confident we can get what we want, which is top four,” he added.
"It goes to show how much we've improved and we have a bit more steel in the team.
"Results went against us on Saturday and that added to the pressure going to Stoke.”
Gerrard also welcomed the return of Daniel Sturridge - who had been sidelined for almost two months with an ankle injury.
He said: "He is a top player with huge potential and he can be whatever he wants to be.
"He can become a world-class player and it is all about Daniel now - does he want to go and grab it?
Gerrard claims Sturridge has what it takes to become 'world-class'
"He looked sharp when he came on and hopefully he can stay fit until the end of the season because with Suarez and Sturridge we are going to score many, many goals."
Liverpool and Gerrard can now prepare for back-to-back Premier League home games - sandwiched either side of an FA Cup Fourth Round tie with either Bournemouth or Burton Albion.
The Reds welcome Aston Villa to Anfield on 18 January, before taking on local rivals Everton in the Merseyside derby ten days later.
