The Liverpool skipper was part of the sides that were beaten by both Italy and Uruguay in Brazil, and some have suggested that the midfielder may now call time on a long-running Three Lions stint.
Taylor told Sky Sports News: "[I would tell Gerrard to] 'Be honest with yourself Steven, just be honest with yourself like we know you are.
"'You do what you feel is right, and if you feel it is right time to retire from international football then retire because you have been an absolutely tremendous player for your country.'
"Steven Gerrard has got great ability [as a captain] that can be used at club and international level, but the club pressure will come more on him to give up the international scene."
Gerrard will be 36 before Euro 2016, and with over 100 caps to his name, there is a feeling that the Liverpool man may decide that enough is enough for his time with his national side.
England's slim hopes of qualification were officially ended on Friday when Costa Rica beat Italy 1-0.
The Three Lions needed the Azzurri to beat the central Americans and also required them to record a victory against Uruguay in their final game, while also needing a win themselves in their last match.
The inquests continue to fly in from all angles as Roy Hodgson's lost their first two group games to record their worst-ever start to a World Cup campaign.
Hodgson's men now take the field against unlikely group leaders Costa Rica looking to at least get some points on the board before they fly home.
Some have questioned Hodgson's position and called for the boss to resign, but it is understood that the 66-year-old will stay on beyond the Brazil tournament.