Born in Redondela, Province of Pontevedra, Galicia, and a product of local Celta de Vigo's youth ranks, Couñago made his professional debut in Segunda División, loaned to CD Numancia, but returned in January 1999 to his first club, failing to appear in La Liga in his first spell.
In 1999–2000, he returned to the second level yet on loan, now with Recreativo de Huelva, after which he returned to Vigo still with no impact (all of his league appearances were made ).
After impressing in a 4–0 win over England at Birmingham City's ground, Couñago was signed by Ipswich Town in the late spring of 2001, as manager George Burley had been in the stands watching his performance. The player, who was out of contract, signed a four-year deal.
Couñago scored at will in his first spell for the Blues, netting twice against Walsall (3–2 at home), Burnley (6–1 at Portman Road) and at West Ham United (2–1, with both teams eventually to the Premier League), and adding a hat-trick against FC Avenir Beggen for the 2002–03 UEFA Cup, in an 8–1 home thrashing (9–1 on aggregate; Ipswich had suffered top level relegation, but qualified for Europe through the fair play award).
Couñago joined Málaga CF in 2005–06, scoring three times in 27 matches as the Andalusians finished bottom of the table. He produced more in the following year, but the club failed to regain its top flight status.
Back to Ipswich
After being released by Málaga, Couñago re-signed for Ipswich on a two-year deal on 13 July 2007, extendable to three if the club gained promotion. Ipswich manager Jim Magilton said of the player: "I have always looked at Pablo as a player with all the attributes to be top class. He enjoyed a good relationship with the fans of this club, but I don't think anyone really saw the best of Pablo in his first spell here". The player stated: "It's great to be back here at Ipswich. I'm really excited about the move. As soon as I knew that Jim wanted me I was keen to come back. It's good to feel wanted. I also know the way Jim likes to play football, pass, pass, pass and that is good for me as well". He scored a return debut goal in the 4–1 home win against Sheffield Wednesday, and added two the following month against Coventry City (same venue, same result).
Couñago was the team's joint-top scorer for the with 12 goals. One of those goals, an audacious backheel in a 1–3 defeat to Charlton Athletic on 8 December 2007, was voted goal of the campaign, also being one of the winners at Town's 2007–08 awards night.
On 21 February 2009, Couñago started his 192nd league game for Ipswich and scored his 50th league goal for the club, in a 3–1 win at promotion rivals Queen Park Rangers (both sides eventually ). In the summer, he turned down the chance to join Swansea City following the arrival of Roy Keane as manager, but joined Crystal Palace on loan a year later, reuniting with former Ipswich boss Burley.
On 6 November 2010, Couñago scored his first goal for Palace, in a 1–2 loss at Middlesbrough, opening his home account on the 27th in the 1–0 win over Doncaster Rovers. In June 2011, aged nearly 32, he was released by Ipswich.
Subsequently, Couñago played five months with Đồng Tâm Long An F.C. in Vietnam, helping the club promote to the V-League during his spell. On 2 October 2012, he joined Hong Kong First Division League club Kitchee SC, for an undisclosed fee; he made his debut for his new team five days later, against Yokohama FC Hong Kong, coming on as a 62nd-minute substitute for compatriot Fernando Recio.
Couñago scored ten goals in 28 official appearances in his only season, and his 30-yard shot against Sun Pegasus FC helped the club win the Hong Kong FA Cup, while he also played a part in its quarterfinal run in the AFC Cup. In May 2014, after one year with lowly CD Choco in Tercera División, he signed for Finland's FC Honka.