Jagielka was in action for Everton against Premier League rivals Manchester United in the semi-finals of the FA Cup on Saturday evening.
The 33-year-old central defender started the tie and played for the entire 90 minutes, as the Toffees lost 2-1.
Former Liverpool defender Carragher was following the match, and he was impressed with the performance of the England international against the Red Devils.
The Englishman has also praised United striker Anthony Martial, who scored the late winner, and believes that Louis van Gaal will remain as the Red Devils’ manager.
People mentioning Stones performance but Jagielka who's not 100% fit has been excellent.— Jamie Carragher (@Carra23) April 23, 2016
Everton didn't deserve that on the 2nd half performance. Martial is a star & LVG is staying!— Jamie Carragher (@Carra23) April 23, 2016
Jagielka has created two chances in 20 Premier League appearances for Everton so far this season.
The former Sheffield United defender has a pass accuracy of 85% and a shot accuracy of 11%, and has won 47 headers, three dribbles and 26 tackles.