Szmodics ended the campaign with seven League One substitute appearances and one FA Cup substitute appearances to his name. Szmodics made his first appearance of the season as a second-half substitute for Freddie Sears in Colchester's 4–0 away defeat to Charlton Athletic in the League Cup on 12 August 2014. He then made his first professional start for the club on 30 August, when the U's were defeated 3–1 by Peterborough United at the Colchester Community Stadium. Szmodics was replaced by Dominic Vose after 57 minutes. Szmodics signed a three-and-a-half year contract extension with Colchester on 10 October to see him through to the summer of 2018. He then scored his first professional goal for the club on 9 November. After coming on as an 81st-minute substitute for Alex Gilbey in the U's FA Cup first round tie against Gosport Borough, Szmodics lifted the ball over the Gosport goalkeeper in stoppage time, scoring Colchester's sixth goal in a 6–3 win. He scored his first league goal on Boxing Day 2014 in Colchester's 2–1 home defeat by Gillingham, turning in Sean Clohessy's pass. Having been confined mostly to substitute appearances, manager Humes admitted that Szmodics had been "very close" to being a regular starter for the club over the Christmas period, and that the player was "very much in our thoughts, going forward". Szmodics then broke into the first-team with a string of starts, beginning with a goalless draw with Crawley Town on 28 December. After breaking into the first-team and making 35 appearances across the season, as well as scoring five goals, Szmodics was named as Colchester United 'Young Player of the Year' in May 2015. After making six appearances in the first team in the early stages of the 2015–16 season, Szmodics was allowed to leave the club on loan in order to gain more first-team experience. He joined National League side Braintree Town on 30 October 2015 for an initial month-long loan. He made a goalscoring debut the following day as his 75th-minute goal earned Braintree a 1–0 win against Macclesfield Town at Cressing Road. Szmodics was recalled by his parent club on 27 November following manager Tony Humes' dismissal by Colchester on 26 November. A foot injury kept Szmodics out of action for several months, wearing a protective boot and requiring injections in order to avoid an operation across Christmas and the New Year.