Born in Logroño, La Rioja, Pinillos graduated from local UD Logroñés' youth system, and joined Racing de Santander in July 2010. He made his senior debuts with the latter's B-team in the 2010–11 season, being relegated from Segunda División B.
On 9 July 2013 Pinillos signed for CD Ourense, also in the third level. He appeared regularly for the side, contributing with 21 appearances.
On 30 January 2014 Pinillos moved to fellow league club Córdoba CF B, and played his first official game with the main squad on 2 March, starting in a 1–0 away win against Girona FC for the Segunda División championship. On 18 July, after appearing in 16 matches during the campaign, he renewed his link with the Andalusians for three years, being definitely promoted to the first team now in La Liga.
Pinillos made his debut in the main category of Spanish football on 25 August 2014, starting and being booked in a 0–2 loss at Real Madrid. On 22 March of the following year, he was sent off in the dying minutes of a 1–3 away loss against Real Sociedad after offending the assistant referee, being later handed a four-match ban. On 11 June, after suffering relegation, Pinillos was released by the Verdiblancos.
In July 2015, Pinillos went on a trial at English Football League Championship club Nottingham Forest, and agreed to a two-year contract with the club on 30 July. He made his Forest debut on 22 August in a 1–1 draw at Bolton Wanderers, and quickly established himself as the club's first-choice left-back. On Saturday 19 December, Pinillos ruptured his anterior cruciate knee ligaments in Forest's 2–1 win over MK Dons and missed the rest of the season through injury.
Pinillos finally made his first-team return for Forest on the 19 November 2016, starting at left wing-back as his club defeated Ipswich 2–0 at Portman Road. Before Forest played their next match, however, the club disclosed that Pinillos required surgery on his other knee due to a meniscus injury that was expected to sideline him for "several weeks".
On 18 March 2017 Pinillos scored his first goal for the club, netting a last-minute headed equaliser against fierce rivals Derby County from a Ben Osborn corner, levelling the match at 2–2. Pinillos had also assisted Forest's first goal that day, with an outstanding cross for the on-rushing Zach Clough to tap in. On 15 May 2017, Forest manager Mark Warburton confirmed that Pinillos would leave the club at the end of his contract on 30 June.
On 2 July 2017 Pinillos returned to his previous club Córdoba, after agreeing to a three-year deal.As of 7 May 2017